Some short, personal notes that I have made on the games:
- LoL is more accessible
Dota 2 is loaded with a lot of stuff that takes ages to get used to, LoL is slightly easier on that regard. It's still a relatively beginner-unfriendly game, but a bit less so than Dota 2.
- LoL is more objective-based
Dota 2 has towers, barracks and Roshan. LoL has towers, barracks(inhibitors), red- and blue buffs, dragon and baron. Knowing the timing for these sets up for more team-fights, which is a good design decision.
- LoL has better hero design (on the average)
Dota 2 has a lot of old heroes from the original Dota mod that have one active ability and three boring passives. LoL rarely have passive abilities in the moveset, which makes the average champion there more fun to play. I still think the best designed/most fun to play heroes are in Dota 2, but they definitely have the worst ones as well.
Dota 2 also has more gimmicky heroes overall(stealth heroes, illusion heroes, Tinker, etc), which might or might not appeal to your tastes.
- Dota 2 allows lane control on an entirely different level than LoL does
Pulling and denies allow a good player to position the lane so that you become hard to gank, and the opposing team becomes easy targets, while simultaneously denying them experience and farm and allowing harassment. You can't really control the lane to the same degree in LoL.
- Dota 2 rewards mobility way more than LoL does
With everyone having access to TP scrolls and smoke, and there being several available attack routes into every single lane, it allows for far more movement options than LoL does, where moving from lane to lane is a relatively time-consuming thing. The attack routes reward aggressive ganking play, while the TP scrolls means teamplay gets a lot easier if the communication is in order.
- Playing support in LoL sucks compared to Dota 2
Playing support in LoL is essentially sitting in lane with your carry and ensuring that he gets farm, and then maybe you'll get a couple of levels in the process. In teamfights you might throw out your ult or something, and then die because you're a support. Warding is a relatively simple matter, but it's still your job. It's a really boring role to play in that game.
Playing support in Dota 2 is an entirely different matter. Yes, it's still your job to ensure that your carry gets to kill shit, but when you've chased everyone out of lane, there are a million other things you can do. You can roam to another lane and set up a kill there, you can stack the jungle so that your carry gets more farm, you can just go out of lane and make people play conservatively. The warding game in Dota 2 is also much deeper than in LoL, and good warding and game sense shifts the momentum to the point that I've made people ragequit by warding and counterwarding better than them. If you're playing a support well in Dota 2(and your teammates aren't retarded), you not only feel like you contribute greatly, you feel like you're one of the big reasons why your team is winning. Can't say I've ever had that feeling if I've been supporting in LoL.
- Dota 2 has more available lane setups than LoL
LoL has 2-1-1+jungle as the only viable lane setup. Dota 2 has like five more of them. Allows for greater strategic variability.
- Dota 2 has a better business model
Others have mentioned this already, I don't think it needs to be mentioned again.
Overall, I definitely prefer Dota 2, but LoL has several strong points that might make it more appealing to you.