Hey Blackcat.
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,
Kie