It really depends on what you're using them for. For me, I use them for drawing. In which case, these are the differences:
Photoshop is made of pixels and can be blurry if the resolution isn't high; Illustrator draws lines using math equations and equations meaning the lines are extremely smooth no matter what the resolution, but are a little trickier to draw. Photoshop, since it uses pixels, can blend colors really nicely; Illustrator uses only straight lines, and though there is a gradient funstion, it doesn't work as well as if you were working with Photoshop. Photoshop has many different methods of coloring a line-art (brush, fill, pen&ink, etc.); Illustrator only uses a pen&ink style for coloring.
In closing? Photoshop is easier to use, can handle a wider aray of techniques, and more flexible, but the picture quality suffers, even under JPEG format. Illustrator is sharper/smoother/crisper, more precise, and never looses picture quality, but it is very different to use and takes longer because it is harder.
Depending on what you use it for, I would recommend Photoshop. It has all the same features as Illustrator and even more, and is more flexible. The only reason I would choose Illustrator over Photoshop is the picture quality. Of course, thats just my experience using them both for drawing. I hope this helps.
