It's more complicated than that - I'll do my best to be unbiased, but, full disclosure, I've been playing DotA for six years and strongly personally prefer it.
Apart from being able to deny creeps/towers (which I personally like, as it raises the stakes of the laning phase), the biggest single distinguishing factor between DotA 2 and League is hero differentiation. In league, heroes who play a similar role will tend to be largely similar - a function of the model, by which very few (if any) players have access to every single hero. Since it's important to keep that from becoming a (blatant) pay-to-win mechanism, hero differentiation is decreased to compensate. In DotA, on the other hand, there are over 100 heroes (currently 90 in DotA 2, I believe), and every player has access to every single one - so, to make that a meaningful number, the heroes are strongly distinguished from each other. Lion and Lina are about as close as two heroes get to each other, and there are still massive differences in both the way they play and the reasons they're played. This isn't necessarily better or worse - I like it, as it leads to a more diverse metagame - it's just different.
The other really big differentiating factor between DotA and League is the way items work. There are no summoner abilities in DotA, but there are FAR more usable items that have an effect beyond their stat modifiers. The biggest single example of this, of course, is BKB, or Black King Bar. Its activated ability makes the user temporarily immune to (nearly) all magic. This completely changes the way the game works in and of itself, for obvious reasons. It's up to you which you prefer.
Other differences are more subtle - DotA doesn't tend to have (I hope I get this terminology right) Ability Power carries, where you can semi-reliably dish out a bunch of damage from a long range. The vast majority of DotA abilities require you to be relatively close to your target to use them effectively, and the exceptions tend to be used for initiation or chasing, so you can get in and use those close-range abilities. This applies to attacks as well - there's only one hero in the game, dwarven sniper, who can attack from beyond the range of most heroes' ability to respond. This leads to teamfights that can be described as 'chaotic', a charitable term for 'clusterfuck' - but a skilled team that's experienced at playing together can make it beautiful.
In essence, my argument for DotA over LoL would be that it's a more complex game with a higher skill ceiling and more interesting/diverse (and well-balanced) competitive play. My argument for LoL over DotA would be that it's easier to pick up and enjoy without taking it seriously. If you have no interest in investing a significant chunk of your life to getting good at it, DotA 2, like Starcraft, is probably worth giving a miss.
Wow, what a wall of text. Hopefully that was at least interesting to you. :)
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Noob asking for help.
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