i use Photoshop for all things, but only because I haven't had enough free access to Illustrator. From what I've heard and the bits I've used, Illustrator is the best for logo, type changes, etc etc. Photoshop can't be beat for mockups, photo retouching and manipulation, and in so many cases for web graphics.
I think Photoshop, with it's pen tool (granted it takes a while to become even moderately proficient using it) is the only one of the three tools mentioned here that's great for all-round stuff. Not as specialized as Illustrator, but a powerful all-in-one.