Oh that DOTA2 vs. LOL thing. Here are some facts:
LOL is bigger than DOTA2 as far as population is concerned.
LOL has a bigger internet footprint.
LOL is more popular.
DOTA2 gives you access to all champs (they call them heroes) at the beginning, you can pay money for ascetics.
DOTA2's map is bigger.
DOTA2 champs have a turn speed. You will see your champ turn to attack a target. Unsuspecting LOL players will say they are experiencing "lag" but it's your champ physically turning towards their target.
Generally DOTA2 players will say DOTA2 requires a higher skill cap. DOTA2 players also look down on LOL players. Here's their argument.
DOTA2 has something called denying. This means you can kill your own creeps, denying your opponent CS. DOTA2 players say this adds an extra layer of skill. LOL players will say that you can deny CS in LOL through zoning and other methods. You can argue that this leads to more exciting play/trades and duals which leads to more exciting game play. Personally, I think can argue both ways, and the whole denying thing is just more busy work/tedious gameplay.
DOTA2 has a death penalty. You can actually lose gold if you don't spend it and you die. There is a mechanic in the game where you can send out a donkey or whatever to buy things for you and bring back to lane. This creature can be killed. This adds an extra layer of complexity.
DOTA2 terrain can be destroyed. Also you do more damage with higher altitude.
DOTA2 has "hidden" jungle shops that you can only buy certain items from.
There are some nuanced differences. DOTA2 people like to say the game has a higher skill cap, but I think it just has more stuff to do. League of Legends tends to have a faster pace to it. It has taken out some of the complexity that some argue doesn't need to be there.
Each game has a collection of fanboys that thing the devs of each game are better. I don't touch that fight.
edit:
On esports, LOL just had their world finals in the fucking Staples center in LA with like 8 million people watching it live during the broadcast from around the world. That shit is crazy.
Also, DOTA2 players are kinda like hipsters.
Says he doesn't want to touch the fight. Calls Dota players hipsters. LoL jk jk.
Your right on most counts. However, high terrain gives a person 100% chance to hit (not including evasion items/skills), while shooting from lower terrain gives a small chance too miss (not counting evasion items/skills). Not damage.
Also in DOTA you can buyback. This cost a lot of money. And was recently nerfed in that 25%? of the time you would've spent dead is added to your next death timer.
Heroes in DOTA also have much more complex mechanics. You can control multiple units in DOTA like a RTS. There are cool mechanics that interact with the terrain. It's really neat.
One thing I LOVE about Dota, probably more than anything else doesn't have anything to do with the mechanics or strategy. Valve really has an attention to detail in this game. There are 1000s of easter eggs and little things like 100s of voice overs for each character. Also to the people saying the game looks like shit wtf. Turn your graphics up. The spell effects have more color in their pallet than all of LOL.
I think both games have their place. I prefer Dota but I always come back to lol for a few weeks every now and then. LOL just feels so stale. DOTA devs mix up the meta regularly to keep the game fresh and that's what I like. The one thing I like in LOL is the dueling aspect. Lane phase is much more important in LOL so you have more chances to 1v1 and 2v2 in dueling then in DOTA. That's probably why I don't like watching pro games in LOL as much. The camera is always all over the place and you never get to see the little nuances of why people win their lanes. I think it's also why single player streaming is more popular in LOL (even disregarding the numbers) than in DOTA.
DOTA players don't think DOTA requires more skill because of denying. LOL players always think that. We just think its a more complex game because of skill sets in the hero and the game physics that's it. Once again, each game has their place and I'm not calling either of them better or worse.
In comparison the the pro scene, while LOLs is bigger, fewer teams get to compete it seems. So if you are looking to get into the pro scene DOTA might be a better option for you.
Just remember LOL players, you are playing the COD of MOBAs. Your COD fish!