Having played warcraft3 dota, then heroes of newerth, then LoL (for the longest amount of time), and now dota2, I can tell you that DotA 2 is considerably better than LoL.
It may seem interesting that League has a level and reward system outside of the game that you can use to gain advantages in your games, but it generally just boils down to a few cookie cutter builds that everyone uses for each specific role, and it's mostly just a business tactic used by Riot to encourage you to spend more money, like Valve's item system but in some cases less cosmetic. In terms of gameplay, either game you play will feel like it has a difficulty curve that starts with a brick wall and transitions into a hill full of landmines and barbed wires. The metagame for league is considerably simpler with its rigidly defined roles that each champion fits into, while DotA2 is much more based around the unique niches filled by an individual hero or small group of heroes, creating many more interesting strategies and opportunities for variation. This also creates a distinct difference in terms of each individual game. Many League games are determined by a very small set of circumstances setting a snowball rolling that can be incredibly difficult to stop, but in DotA, teams can feel VERY strong early or mid-game, but have heroes that all fall off if the game goes on for too long, creating openings for smart and skilled players to get back into the game.
In terms of polish, Valve has done an amazing job creating a game that, when compared to League, feels professional and well-made. Which is a nicer way of saying what Skin said, although he is basically correct.
