I think Dante will randomly dodge in any direction if you just press either of the bumpers, and in the air he will just dodge in place, doing that flip thing. So the analog stick is simply for a more precise dodge so you know exactly where you want to dodge to.
I don't think the dodge is all that broken, because yes, you might still get hit anyway if you don't dodge correctly. But, like I said, it is much more emphasized this time around... and much like in Bayonetta, they are aiming for you to use it more often. Hell, you even have the demon dodge now, which gives you a power up. The only thing I remember something like this happening in DMC was with Nero and his table hopper move thingie... which I never even used since all it did was give you three extra dodges after so you looked cool, but it was the most useless thing in the world.