It all comes down on you.
First, although both games are equally hard to master (zoning is a ***** in LoL and can only be tammed by the bravest of players, but Denying and counterpicking will leave the best strategy on his knees begging for mercy in their first run), LoL is much easier to get into, because there are less mechanics to learn(not any less complex, just less). Also, the Meta, that is, the function each champion should take and the position of said champion in the game world, is less of a burden than in DoTA, because there's only one (with much more possible variations than in DoTA, but that's pro stuff, so, later on). So if you want to be able to pick it up and enjoy 70% of what's to enjoy in a game instead of 35%, take LoL. If you like the RTS way of playing, starting completely hopeless and pathetic and learning each little mechanic as you go along, then take DoTA.
DoTA's playstyle, however, is much more reliant in you. It's easy to deny your opponents, and the slightest lead will make you way ahead of your enemy laner (considering that you lose gold when you die in DoTA). You can 1vs5 their team if you're fed enough, and single handingly carrying directly is possible.
LoL' playstyle is very, very team focused. No 1vs5 enemies, no snowballing without control, but on the other hand, everyone has a chance. The higher you go on DoTA, the more obvious it is that the game is decided in the champion selection and in the first minutes of the game. You can make comebacks, but that's much more likely to happen in LoL.
LoL tends to reward the team with the advantage, while DoTA punishes the team with the disadvantage.
So if you like team related games and/or have some friends playing, take LoL. But be advised your team can be your downfall, and it's hard/impossible to carry 4 people.
If you like to be "The Hero" and play solo, take DoTA. Just remember it's not as fun when being in the opposite team of "The Hero".
Remember, balance is much different from both games.
LoL tries to go to a "everyone's balanced" rule. Mostly it works well, and champions feel unique in playstyle but most of them never feel blantaly overpowered (Release Xin Zhao and Release Vayne were exceptions, but they have been dealt with). However, any champion who happens to be "toxic" (that is, having a low-risk, high-reward mechanic which is very, very hard to counterplay), it usually gets the wrong end of the stick, like Heimerdinger, whose turrets granted him a lifetime of unviability and a rework incoming, or pre-rework Evelynn, who was basically the LoL equivalent of a meat-made submarine designed to search the bottom of the ocean, because she was very good at surprising people from behind. So you must be ready for finding a champion who is in a bad spot.
DotA, on the other hand, has a different philosophy. Everything is unbalanced, so everything is balanced. As such, every champion is absolutely crazy OP, so it works. However, it leads to a scenario where if a champion is more OP than everyone else, you don't really know what to do. There was a time where Nightstalker was the shit, and no one knew why. Maybe it is the super duper attack/movement speed buff always on, maybe it's the silence, maybe it's the fact he goes completely batshit crazy at night, but he was way to powerful and stupidly simple to play (farm all day, wait until night, then rape everyone). Not to mention that it means that a hero who is behind his opponent (which happens a lot, given the snowbally nature of the game) will feel mostly powerless to stop it.
Finally, strategy-wise, it's day and night. LoL focuses on champion sinergy and counterplaying the opponent, and the moments of truth happen during mid game, but are much more subtle (letting your opponent kill 2 Dragons is basically inviting them to steamroll you), while DotA's moments of truth happen during early and late game, mid being the glue which holds these two together, and DotA focuses on counterpicking and adapting to your opponent. DotA's all about preparing to the teamfight, while LoL's teamfights, albeight shorter, are much more intense. The action happens in the teamfight, not before (In DotA there are two unnoficial phases, the Pre Teamfight, where the heros prepare their skills and tend to prepare their strategy, and the Teamfight itself, which is a consequence of the Pre Teamfight and it's almost impossible to turn around, sort of like chess: you plan your move and the moves ahead, and if you planned wrong, it's almost impossible to comeback. LoL has three phases - The Pokefight, where champions trade long range shots and keep their distance, and the tanks search for a possible initiation chance, the Teamfight, where the action happens, and the Aftermath, where the winners pursue the surviving defeated, because if they reach their base to regenerate and defend, shit can hit the fan fast. It's like an RTS: planning is still a very important skill, but how you react to your environment will be the most important factor).
I myself prefer LoL, but in the end, you will have to choose for yourself.