GTA is one of the best games for gamepad, barring any ultra-competitive PvP ambitions of course. Even then I enjoyed Free-aim PvP and getting a few kills fighting top-notch mouse players. They could kill me a bunch of times but as long as I got a few kills with my controller I didn't care. The average mouse players I'd eat for breakfast, with Elite Controller and custom profile which improved fighting by 100% over the old Xbox 360 Controller. The one weapon and situation where mouse and controller were more or less level, was heavy sniper at very long range. My profile allowed very minute and gentle corrections that aren't so easy with mouse unless you have various and excellent DPI settings and use them well. It is also probably the one situation where the slower strafing with the controller was actually an advantage over the faster strafing/change of direction with keyboard. As the distance decreases, that changes in favour of mouse again.
Vibration really does make it more immersive. Thunder, the rumble strips on the sides of the road, explosions etc. Like ic1male I prefer controller where possible. Comfort and immersion, and not having to be the best, makes it more fun for me. Plus I get a bit dizzy with the mouse as it can be a bit jerky as you turn or aim quickly. The controller makes that smoother.
