First of all i'd like to mention out that, since this is purely an opinion game where we debate on what is better or worse and why. Many people have had their claims on facts that have a hold in them but I will write down my own opinion according to what I've played and experienced.
In overall I've had around 6000 hours of mobas played alltogether. I've played Dota 1, Dota 2, Heroes of Newerth, League of Legends, Smite and Heroes of the Storm. Primarily I will talk about Dota 2 and League of legends with a scoop of Heroes of Newerth.
Now before some of you can start having a cringe at me for saying Heroes of Newerth as it has had an excessive amount of toxicity beyond League of Legends and Dota. I am judging that by swearing, insult and hatred per game and I can easily HoN took the cake in that. Despite all of that, it's what got me more into the MOBA genre.
Why I like Dota 2? What's the good and bad about it?
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Lets start with the positive:
1) It punishes you heavily and makes you lose gold. (this can be a negative thing to people)
2) It has runes that can change teamfights and or cripple the enemy from making a move because someone has a specific rune.
3) Has the possibility to make ganking on a whole new level. By either having a smoke of deceit (to turn yourself invisible until you reach a certain range to the enemy hero) or by aquiring an invisibility rune or Shadow Blade (insibility active item)
4) If you are a lone wolf and a proper carry yet have a sense as a teamplayer, you /can/ singlehandedly win the game for the team.
5) Free language learning tool (mainly for russian, sometimes chinese)
6) The variety of heroes the game has to offer can make you change your gameplay style just because there might be a specific hero in the game.
7) e-Sports is fun to watch along with the Allstar and troll matches they do.
😎 Pause functionality, if enemy team or your team doesn't troll you when someone really has to move away from the pc for a moment quickly.
9) Possibility of punishing your enemy with denying your creeps with autoattacks and making him or her lose income.
10) All heroes are free to play in the game.
11) Possible to buy as many wards as you want in the game and use them, they only have a cooldown timer until you can buy another set.
12) Possibility to counterward and punish enemy team, to not being able to see your team for awareness advantage.
The negative:
1) Supports can get severely handicapped if they are constantly being picked out, making them incapable and scared on taking bigger steps.
2) Not the most starter-friendly to people who have never played or played to a very minimal amount of MOBA genre prior to it.
3) In EUWest terms, having a full English talking team is a rather rare or uncommon occasion, to be able to have team strategy or communication can be heavily limited
3.5) In US It's easier to get an English speaking team, however there seems to be slight bit of additional toxicity with whining brazilians.
4) This can be a bad thing if you're playing with your spouse who might not have the best temper.
5) Last hitting has a tiny delay, which you have to consider your character animation to properly start and finish for the hit to count.
6) Making a player leave in a match is more common than in League. Just throw them on a cliff and not allow them to teleport back. hee..hee..hehe.
Bonus:
1) Buyback functionality. This can be both good and bad because teamfights can start off with heavily and when heroes die, they can use their gold to buyback themselves and get quickly back to the battle using teleport boots or teleport scrolls to nearby towers. This can be a minus in terms of teamfight fairness but they pay a price for that possibility.
2) Playing with jungler heroes are rather easy to use and jungle is pretty straight-forward on clearing the camps and gaining the exp and money to benefit in aiding your team later on.
3) In-game voice mic possibility. (this can help if your PC or laptop is a bit old and has issues running other programs in the back and reduces the amount of computer resources required to talk with someone to make fast decisions).
4) Graphics look pretty yet takes a lot of more resources to get it maxed out for eyecandy reasons.
Why I like League of Legends? What's the good and bad about it?
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The positive side:
1) It's friendlier towards players who have from small to no experience at all on learning how to play a MOBA game.
2) Gameplay mechanics are easy to understand but have a large learning curve until being able to use its full potential to your advantage.
3) Teamfights make the difference in the game, unless you're super fed. Although, you are more depended on your team than being a lone wolf. (Unless you are rengar and making my day a nightmare..)
4) Lasthitting is easier.
5) Every champion is easy to play but has a learning curve attached to them, to make big plays you have to get a better grasp of the champion.
6) Supports are loved in this game a lot, supports don't lose money if they die, supporter role items can benefit the team a lot.
7) No punishment given besides a time penatly for dying.
😎 If you're at a stalemate on how to approach at an enemy team then the game has objectives that you should strongly consider taking to gain a better advantage over your opponent. Those would be the Dragon buffs and Baron buff. Those buffs give you a significant boost and helps you deliver more devastating blows, stronger minions, additional hp, faster regeneration on both mana and health.
The negative side:
1) All champions have a cost to them, you can unlock them with either real money or ingame points(IP).
2) You can't be as much of a lone wolf, you should stick to your team more often.
3) No voice chat option
4) E-sports as of late has been rather dull.
5) Warding is very limited. Not a lot of people usually buys them and they are usually limited and in late-game wards are blessings if you have them.
6) With certain champions, if you have certain skins you can actually have spell effects and their size fooling the enemy player. For example Zombie Jinx has small traps and if you think you can squeeze through the gap, most likely you won't.
7) Jungling for a beginner is slightly difficult and a downfall. They don't have as good awareness, knowledge of how to keep track of enemies and when is the right time to gank.
😎 From the course of time I've come to realize that in especially Diamond level games, if each lane starts out horribly, there is a very small chance to even remotely have a comeback chance unless the enemy team pulls a 180 and starts throwing the game away in their favor.
The bonus:
1) Bush hiding is an interesting feature and can allow ganking rather easily.
2) Elixirs can boost your physical or magical damage.
3) It has summoner spells with a high cooldowns to assist and aid you in fights and defending.
4) Aquiring baron and dragon buff makes you a BAMF.
5) Doesn't require you to go on a noodle diet to max out graphics, even at maxed out it looks pretty.
Conclusion:
Now i'm not going to turn the tides by saying 1 game is significantly better than the other. They both have their positives and negatives. It is completely depended on which one suits the style you want to play in.
Dota 2 has the upper advantage if you want to be able to destroy your opponent by punishing them constantly and the game rewards people for it. The game also has in my book a lot more opportunities when it comes down to having a wombo-combo teamfight in destroying an entire enemy team quickly or making the teamfight already decided. If you are a carry and near the end game, you can single-handedly solo the entire enemy team if the position is just right. Same goes for certain supports like Rubick, Earthshaker, Sandking or Witch doctor. It is not the best choice for newcomers as it has its own niches that can make it harder for a newcomer to pick the game up. Dota 2 gets my vote.
League of Legends has the upper hand when it comes down to starting, playing and learning easy. The game rewards you if you start to get a hand in the game mechanics and mastering champions.
This does not mean that how the high-tier players handle it. Now when it comes down to high-tier players, both Dota and League can make the game very difficult for you because players at that stage already start counting how to read time, what usually the jungler does and who is roaming, when he /might/ be in a threat and so on. Dota however has more of the element of surprise since despite having wards, having an invisibility rune or a smoke to cloud you from detection, you can make ganks happen a lot easier and push the game more on your side easily. You don't usually see your supporter roaming from bottom lane to top lane.
E-sports however have it way differently. League seems to be super serious about everything and the Koreans are the biggest superstars from what I've seen (SKT for those who know them). League does have it's own fun moments when they do allstar matches, or a 1v1 team red vs blue in howling abyss game. To me that seems the only small part of fun, the main event is still 5v5 on Summoners Rift and from watching many years now, to me it just seems to get boring and boring. Occasionally there are fun matches that are good to watch but usually it's very strict on what will get picked and you think to yourself. Oh damn, I nearly saw this exact same lineup not so long ago. Dota seems to make it a bit more fun, they have additional things programmed in after the main event and it's pretty fun to watch and how the players keep it chill. They seem to have a bit more options when it comes down to picking something, they do repeat the same strategies often like on League just because it's meta and they know how to play it because they want to be sure with what they play with they are certain they have trained for it in practise.
TL;DR ver. Dota 2 takes my vote in allowing me to punish the enemy and for me to suit more into my kind of role and style of the way how I like to play it.