Logo

I'll make it simple for you
Illustrator is working with VECTOR in most of the times.
Photoshop is RASTER in most of the time, so If you're not going to retouch any picture and you just going to make some clear logo I'll recommend going with Illustrator, Yes you can do it in Photoshop but you know :D Photoshop is most likely designed to retouches etc not logo making program :D

For me I'll combine these 2 programs I would make some great logo in Illustrator and then finish it in Photoshop by adding some final touches like color correction etc.