I am in no way a pro of MOBA's, but I hope my advice will help you out.
So, The first thing for you to do is to download both games and try their trial/training modes and then decide which one you feel like being "your thing". You won't get the full experience (like, I dunno, PLAYING WITH OTHER PEOPLE) but it will give you a basic understanding of games' mechanics and will allow you to understand which one you like playing more.
But if you would like to read an opinion of another person, then:
I prefer DOTA2 to LoL. It has:
-More appealing (for me) design and selection of characters;
-Greater speed (not the of match time itself, but of attack animations, effects and stuff);
-Supports seem to be of greater use;
-Higher difficulty, but also greater satisfaction from victory.
-All characters avaliable from the start. But if you DO want to limit your selection, then pick Single Draft mode, where everyone can pick from one Strength, one Agility and one Intelligence character (or all random mode).
So, pick whichever you want, but if you do pick DOTA2 as your main MOBA, for the sake of everything holy, DO NOT play Invoker and Meepo untill you get enough experience, because those guys are HARD to play.