I have played about 600 hours of Dota 2 and even more of League of Legends and I must say that Dota 2 is the better game here. They are both excellent competitive multiplayer games and, while League has a bigger variety of game modes, it is the classic 5v5, three lane map where it is at. And Dota is built around that map and there are a lot of heroes that would not just work in any other game mode. And this dedication to the classic game mode is what makes it better than League.
Because of said dedication, a player has more options and available tactics at his disposal. Rune control, better split pushes, more interesting hero ability design, higher mobility, a bigger emphases on hero synergy, a more interesting meta game etc. My point is, that while League is more friendlier to newcomers of the genre, once you get into Dota, it will be hard to go back to League of Legends. And I say that as someone who still goes back to League from time to time and wishes that he could buy a town portal scroll.