The controls feel "sluggish" to you because all heroes have turning speeds.
Unlike LoL, the heroes in Dota 2 don't instantly turn 180 degrees when you want to change their directions. This allows mechanics like Pudge's hook to not be broken. Imagine you're chasing Pudge only to have him instantly hook behind him. Because of his turning animation, you can tell that he is about to turn around to hook you.
Each hero in Dota 2 also has their own attack animation with different wind up times. Heroes like Sniper, Anti-Mage, and Faceless Void have fast attack animations that make it easy while other heroes like Crystal Maiden and Drow Ranger have slower attack animations that make it harder to last hit. It's all there for balance reasons.
On Dota 2's balance...
...please don't talk about the game's balance unless you have a deep understanding of the game. The game is balanced for competitive play, not for common pub play. All heroes are situational, and they can all be countered. Even if you don't have the right hero to counter the enemy you can still buy items to counter that hero. Obviously, it's not perfectly balanced, but IceFrog does a really good job. He buffs more than he nerfs, and if he ever nerfs he just makes the hero weaker in an area that's different from what made them strong (i.e. Lycan is a crazy pusher, but IceFrog only nerfed his jungle.)
What I really love about DotA and Dota 2 is that it allows players to make choices. The hero pool is very diverse, no heroes overlap unlike some champions in LoL. The meta is open, and there are many, MANY ways to win a match. Unlike Riot, IceFrog embraces change in the meta and tries to incorporate the changes.
Viable Lane Compositions in Dota 2 ("bot"=long lane, "top"=suicide lane):
1. 2 top, 1 mid, 2 bot.
2. 1 top, 1 mid, 2 bot, 1 jungler.
3. 1 top, 1 mid, 1 bot, 1 jungler, 1 roamer.
4. 3 top, 1 mid, 1 bot.
5. 1 top, 1 mid, 3 bot.
6. 1 top, 1 mid, 1 bot, 2 jungler.
7. 1 top, 1 mid, 1 bot, 2 roamers.
8. 1 top, 2 mid, 2 bot.
9. 0 top, 1 mid, 2 bot, 2 junglers (OPA Na'Vi style!)
Viable Team Compositions:
1. Heavy pushing.
2. Heavy ganking.
3. Four protect one.
4. Two carries.
5. AoE.