First of all, let me make clear that I do not intend to pull the sardines to either side, just explain a little of each and put the experience I had in each of the table.
What is MOBA?
The MOBA or multiplayer online battle arena, came up with a modified map of Starcraft called Aeon of Strife by a player, which inspired a Warcraft player to create a map called Defense of the Ancients (or DotA), after opening the code several maps "in DotA style" were created, then joined and improved by several people, but the name that stood out was the IceFrog , name that is still very remembered by the players of the first DotA.
DotA
Because it is a modified map within another game, DotA had some cons, as need another game, have no tutorial or introduction, making the entry of new people more difficult.
The gap between the first and second DOTA, was almost 10 years and was developed by Valve with Icefrog. In this new game already has a tutorial, and some things have become more self explanatory, such as the tree items that are possible to be created, but the game is not that easy to get started without a previous game luggage (and can I say this from experience, since I played 2 without playing 1).
The graphics of the second game evolved considerably from the first version, and maintains a means somberly.
DotA can be purchased through Steam for free.
League of Legends
League of Legends or LoL foo developed by Riot Games along with some developers of the original DotA, who left did not agree with some directions that the original game was following.
Being a new game, the ease of someone who has never played MOBA start playing LoL is much higher than DotA, because this has a more complete teaching mode, and is entirely in Portuguese (in DotA only the voices are not in en), which can be an advantage for many.
In LoL champions are released 10 per week. You can purchase champions, so you can play them whenever you want, they can be purchased with real money or play money.
The LoL chart is more cartoony and colorful.
League of Legends can be acquired for free through the site Riot .
My experiences
As I tried to make it clear up there, the two games are very similar in style, and even emerged from the creators, and there are more MOBAS, but I stopped here in the two "major competitors". That said, I believe it is only a matter of personal taste, or even what your friends are already playing.
My friends played DotA 1 in college, but never interested me, was a very complex game called not far from my attention, though they insist for me to play. Years later, already formed, he left DotA 2 and they were crazy and once again tried to pull me. After much insistence I decided to try, and found it very difficult, having to decorate various items and skills and combinations, and at first did not give much attention, but playing with them sometimes.
After a while I began to want to play more and more, and now I'm addicted, despite being far from their level, but I play well with some characters.
The LoL I must confess that some tried three times, but not enjoying it. Not enjoyed the chart, and do not get me wrong, I love cartoony games (like The Curse of Monkey Island, several Nintendo and etc.), but simply not enjoyed the look of LoL, I found a little confused at the time of the struggles, perhaps because all very colorful could not make out what power was who, and did not play enough to get the builds. But I not tried so hard, even for already enjoying DotA and not wanting another MOBA.
Well, that's just my opinion and can be very different from many, so I would like to know the opinion and experience of you.