I have played League of Legends for ages... But Dota 2 is simply a much better game in every possible way.
I played LoL only very briefly (about 2 weeks), and really only installed it because it was free and I was vacillating on whether to trade or keep my Dota2 beta invite. I had never played the genre before and found the tutorial very helpful and the humans vs bots MM a good place to start. I had time to get comfortable with only a couple of characters, but I did enjoy it to some degree. LeBlanc mid was my shit.
That was in December, and I've been playing Dota2 since January. I find Dota2's artstyle "modern" and really makes LoL look dated. I mean, really dated...no comparison at all. Also, I feel like the gameplay and tactics are more diverse than what I experienced in LoL...but I'm not sure, since I didn't play LoL nearly as long. Still, there just felt like there was a lot more to learn in Dota2. I also appreciate that all the heroes are free and that purchasable items don't modify the gameplay experience.
Lastly, Valve really seems to be kicking ass with their support of the game and pro scene which is a rare sight and one that deserves extra love. Valve really does TF2 and Dota2 right with the constant updates, fast bug fixes and consistent up-time. When I think about the last few weeks of Diablo 3, I can only tip my hat (less players to be sure, but that doesn't make me feel better when my experience is shitty by and large).
Dota2 is the clear future of the MOBA scene, IMO. Nothing else is or will be as wells supported as Dota2...and nothing else is as modern as Dota2. Valve has this generation locked up for years to come, and as such I'd recommend that anyone who enjoys the MOBA genre to start putting in some Dota2 time. Don't switch if you don't want to, but don't SKIP Dota2 either. Who gives a shit if you don't have friends playing Dota2 yet? You make them as you go along...like anything else in life.
$0.02