For around two years there are 2 main, leading MOBA Games: Defend of the Ancients 2 (DotA 2) by Valve and League of Legends (LoL) by Riot Games.
I tried both of them and both are great games ! Really. But which one is better ? That is the question I am going to answer in this article.

I will be comparing exact aspects of these 2 games to give you a nice comparison. 

1. Heroes/Champions
In DotA 2 everyone can play any hero since the very beggining.
In League of Legends there is a every week Free Champions Pool and to play champions that are not included in the pool, you have to buy them using coins you earn while playing games called IP or points that you can buy called RP (Riot Points).
Summing up, DotA 2 is definately better if you want bigger amount of heroes available since beggining.

2. Newbie-friendly.
In DotA 2 you will see a lot of people that won't accept a fact that you are new and you are learning. They want you to be expert immediately. So prepare yourself for some criticism. Also DotA 2 is a lot harder game since beggining, because even Level 1 can be matched with Level 100.
League of Legends is definately more newbie-friendly. It's definately better to start your MOBA Career with LoL and not DotA 2. In LoL more players will understand the fact that you are new. Also, you will be matched with players at your skill level.

3. Items and mechanics.
DotA 2 items are definately more complicated than LoL items. Also, there is more items than in LoL. What is more, in DotA 2 you can't teleport back to your base for free - in LoL you can. To buy proper items in certain situations, you have to be playing DotA 2 for at least 6 months. In LoL you have detailed and updated guides that will tell you what is best for you. There are guides in DotA 2 aswell, but they are so outdated.
However, in terms of mechanics, I trully believe that DotA 2 is a better choice. Why ? Because of Runes system in LoL. It's really complicated and people who can afford runes have big advantage over people who can't. It's a little bit of PayToWin in my opinion, and that's not fair.

CONCLUSION:
In my opinion, if you are new you should start with League of Legends. This game is pretty much noob-friendly and here you will learn basics of MOBA Games. After you play it for some time, you can try DotA 2, which is, in my opinion, a harder game. However, I prefer DotA 2 than LoL, just because of Runes system in LoL, as well as a cap at 30 level.