The tool you choose to use should depend solely on the
screw you're trying to turn. Same goes for designing Web projects. When beginning the design phase of Web project X, final deliverables should be taken into account when
deciding which application to use. Every designer I work with is equally proficient in both Illustrator and Photoshop; while I'm sure every creative has their favorite, both are tools that can be wielded with awe-inspiring deftness. Will the final project hit the Web as XHTML or rich media? Or some amalgamation of both? Making this determination prior to design kick-off can save HOURS of design translation, giving your project a much better chance of coming in on time and under budget.
The formula is absurdly simple:
Flash / rich media = vector = Illustrator
XHTML = bitmap = Photoshop
I submit the responsibility to pose the question is shared. I will try my best to remember to ask - but as long as SOMEONE asks, that's all that matters.