Competitively, Halo and League of Legends are basically the same game.
"Okay Audley, you've gone off the fucking deep end. How can a first person shooter with equal starts and a top-down MOBA with 100+ champions be the same game?"
I'm going to start off with extremely generic descriptions, but transition into more complex facets of play that exist in both titles that players may be completely unaware are parallel.
The team is more important than the individual. In both games, it's extremely unlikely one player will single-handedly carry the game. Furthermore, a team of 4/5 players that work together well are more likely to win than a team of 4/5 players that have superior skills, so long as the individual skill gap isn't enough to outweigh the teamwork team's ability to execute at all.
At the start of the game, both games have a generic win condition. Whether it be "Destroy the Nexus" in LoL or whatever the game type in Halo it is you're playing, there is a condition for victory.
On your way to the ultimate victory, there are smaller conditions that must be executed to accrue an advantage to set you up for that victory. In Halo, this is generally related to map control and power weapons. In LoL, it can range from taking towers and Dragons to item powerspikes, to certain level breakpoints that give you a certain skill powerspike.
Depending on your current circumstance, your actual "win condition" may vary wildly. In LoL, some team compositions simply reach a point that they can no longer be fought. Others rely on pressuring advantages early to get a large enough lead to overcome later troughs. Some rely on team fighting, while others rely on avoiding team fighting at all costs. In Halo, your win condition is not always "reach the max score" -- but simply to have a high score than your opponent. Near the end of Oddball games, you may simply try to keep the Oddball in a neutral location to keep the opponents from racking up score while you sit on a lead, rather than try to hold the ball yourself.
Information wins games. Both are imperfect information games, where you know for certain where you are at any given time. LoL gives you a minimap with other areas of revealed vision (allied towers, allied champions, allied wards). Halo gives you icons that show whether your teammate is in combat or not. But neither of these are enough.
You still need to know where your enemies are, whether through warding, pinging or calling out their location. You need to know what weapons or major cooldowns players have available to use, both on your own team and on the enemy team. These bits of information get fed into you through communication in games and empower you to make better decisions on where to go or what sort of plays you can potentially get away with attempting. Aggressive plays while the enemy outnumbers you in an area get punished, but knowing the enemy are concentrated on one side may let you know you can jump out and out-BR the fellow in the rocks (or all-in the enemy top laner and take his tower.)
Each game has lanes, and a blown lane assignment must be compensated elsewhere. Halo's lanes aren't as pronounced as League of Legends, but if you examine the successful competitive maps carefully, there is a general trend of aisles of play with segmented sightlines that force map areas to operate in a nearly linear fashion. On certain maps (Sanc, Pit) if a team takes map control from one “lane”, the best way to offset that is to press your advantage in another lane and “flip” the map to neutralize the bleed caused in one lane. In LoL, you'll often find successful solo queue junglers abandon losing lanes and attempt to snowball lanes that are doing well. Or in competitive LoL, you'll see teams that lose an objective on one side of the map often attempt to mirror the objective on the other side whenever possible.
When you're leading, you want to get further ahead. In LoL, this can mean continuously beating down on your lane opponent, taking objectives, or simply getting wards in the enemy jungle to track his movements so you can continue to execute. It could mean forcing a team fight, or overloading another lane while your opponent tries to catch up in your lane. Snowballs are common and easy to spot in LoL.
In Halo, snowballs come from two things: power weapon control and spawn killing. If you've got a numerical advantage, you push, you take over map control (or grab a power weapon). If you've reached the enemy base, you take their flag (and run it wherever their numbers are going to be weakest once they spawn.) Whenever possible, you kill the people as they respawn to avoid letting them influence whatever play is currently happening. You never drop an empty enemy Sniper in H2A, to keep them from ever seeing their rifle again. You always try to position in a way that will influence enemy spawns in a way that make killing them like fish in a barrel.
Sitting on a lead leads to comeback opportunities. Pressing an advantage leads to frantic decisions, forced mistakes, and steeper advantages.
When you're trailing, it's better to stall out than to try to force plays against the team with the advantage. In LoL, attempting to team fight at Dragon while down a few thousand gold in the mid game can turn into a dire situation of being aced and hemorrhaging towers. You can often offset leads by getting small areas of vision control and making a pick-off to slowly ease the gold lead into your favor, while champions with waveclear keep your towers safe. The longer the game goes on in LoL when you are trailing but avoiding giving up larger advantages, the less that flat gold advantage means as the percent advantage decreases.
In Halo, if your opponents have map control or power weapon control lorded over you, it's often best to play passively until your opponents overextend, and retake map control while you've gotten a numerical advantage. Map and weapon control are fluid, and avoiding hemorrhaging kills will allow your team to either take over new focal points on the map as weapons respawn / hills move or to take over the strong areas of the map to set up to slay your opponents and close the gap.
Team compositions are important. In LoL, it's pretty obvious that you don't want to run a team with 5 Marksmen. Such a composition relies on nearly perfect play to be able to execute a win, and the susceptibility to enemy burst or crowd control can leave you in big trouble. You generally want someone to tank, someone to support, a mage/assassin with damage from spells, and an ADC to deal damage with clicking (and probably double down on the tankiness).
In Halo, it's less obvious, and although many pros deny the existence of roles, time has shown again and again, rosters with a player dedicated to Sniping (ADC!), one generally dedicated to “selfless” plays (support) (flanking, objective-running), one player balls-out aggressive with a dominant BR (tank/bruiser), and another dedicated to controlling certain areas of the map (control mage) tend to have the most consistent high placings. Teams made of players of similar styles often struggle, and teams made of lesser skilled players with a decent composition often out-perform expectations.
Speaking of controlling certain areas of the map, Zoning is an important aspect in both games. In LoL, zoning usually refers to a player with high burst potential or CC / Engage potential standing in a position and using their presence as threat enough to keep a damage dealer from moving forward (or in some cases, like Alistar W, using the ability to keep them from coming near Baron while you finish off your smite.) Zoning can also accrue you advantages in minion kills or experience during the laning phase by keeping the enemy away from the minion wave.
In Halo, zoning is what makes Ogre 2 great. Whether he's controlling an actual power position or a portal on Warlord and watching cross-map sightlines, he's often in a position to keep other players from threatening his team, while staying relatively safe himself. Players also often use grenades to cut off a route or impede an enemy's advance moreso than to actually attempt damage. In H2A's King of the Hill on Warlord, controlling the base counter-clockwise from the hill often meant the best sightlines to assault the hill, while also great amounts of safety from the players spawning directly opposite of the hill's base – able to force those players into a less optimal path in order to advance for the objective.
Both games also emphasize Spacing quite heavily. Again, Spacing is something more prominent / known in LoL than in Halo. It generally refers to the distance between you/your teammates compared to the distance between you/your enemies. This mostly comes into play during laning phase and team fights. In bot lane, you usually don't want to attempt to trade when you are in range of both enemy laners – you want to trade while you+your ally are in range of the enemy ADC, but not in range of the support. This ensures you have more damage potential on a single target than you would with improper spacing. Qiao Gu demonstrate the power of teamfight spacing with the synergy between their mid laner and ADC, who are almost always in position to focus the same target in a teamfight.
In Halo, you'll find the more successful teams often talk to each other on positioning, and communicate whether they have another's help or not. Less successful teams focus on enemy positioning entirely, and don't focus on whether or not they have the ability to cover each other's sightlines. This also ties back into the aforementioned “lanes” of Halo – you can see OpTic Maniac often shift to the opposite side of Shrine off spawn to cover an uncovered lane while also guaranteeing he has additional angles on players his teammates may be fighting. Coach Towey of Evil Geniuses does a great job coordinating EG's ability to cover one another and ensure they are spaced well.
In both titles, if you were to make a sort of imaginary venn diagram of your potential damage / engage ranges over the course of an entire game, you'd likely find the most successful teams have the highest concentrated / most occurrences of overlap whenever they're in combat.
Mobility is survivability.
This aspect of both games is both accepted and entirely overlooked simultaneously. Sure, people acknowledge Flash is almost 100% must-take on most champions in LoL. They acknowledge that the amount of champions with dashes or hastes in their kits has been gradually increasing over time. Halo players acknowledge Sprint gets used defensively more often than offensively. And that often, attempting to chase is more dangerous than attempting to flee. But what they don't seem to acknowledge is the amount of damage you can avoid simply by being mobile.
Dodging engages in LoL with a blink, staying just-out-of-range of those melees through the Captain's aura from your Janna as you flee toward her with 18% increased movespeed...every missed skillshot or second you stay out of range simply by moving, you've given yourself additional survivability that can't be directly quantified. Is 20 movespeed worth more than 200 health? If it gets you out of the way of that Morgana binding, it absolutely is. If it helps keep you 50 extra range out of the way of Annie's ultimate as she activates Talisman and starts booking it straight for you, it is.
In the upcoming Halo 5, the Thruster Pack and Sprint combine to add so much additional survivability (even with the cost of delaying your shield respawn, it gives more than it takes). Grenades lose relevance as player mobility increases (limiting them almost solely to zoning potential or spot-checking). Close range combat becomes a battle of who can out-maneuver the other, with several areas of low ledges offering potential to parkour your way out of there with a combination of clamber and thrusters. Hell, even being able to get from one location to another more quickly can mean you snagging the power weapon before your opponent, or getting clear of a line of sight before an opponent has a chance to set up a shot with their sniping pick-off tool. Projectile weapons like the Plasma Caster are not much different than a LoL skillshot, and with the leaps granted by the Thruster, this means your best tool to survive isn't whether or not you have shields, but whether or not you can dance.
I truly believe that, at their core, almost all of these aspects of gameplay can be applied to any competitive title (and actually, to any team sport in existence) – LoL and Halo are just the two I have the most experience with and can generate the most examples of overlap from.
While I don't feel I am THAT mechanically skilled at either game (I honestly can't aim for shit in Halo), I take an analytical, measured approach to playing both and focus on playing smart over playing well. I am currently Diamond 4 in League of Legends and have coached a few pro and amateur Halo teams. I also never lose a matchmaking game of Warlord King, by applying the LoL concept of Zoning to every game I play.
Thinking about games in terms of overlapping concepts can help you improve your individual and team-based play and help you see a marked improvement in your ranking.