hello, im doing some research on these two programs for my EPQ, can you pretty please answer my poll? :} if you reply and say why or explain something that'd be great too. sorry if this is in the wrong section aswell.
Answer is both as I think in many ways it's the cross functionality of the Creative Suite that makes it so industry leading.
It's good drills to use Illustrator for things like logos because of the vector format - scalability etc. That said, I'll often work between the two, PS for it's versatility for things like photo-manipulation and certain effects. Indesign is also a very useful bit of software - but you didn't ask that so I'll stop waffling.
Hope this helps, happy to elaborate more if you need,
Maybe you might be better not asking such a vague question as good research comes from asking good questions. There are a lot of good answers here though as people have explained some of the reasons why there use one or the other. I happen to use both pieces of software, but I would expect so do most other designers!