The number one difference between these two superpowers is resolution. The true test of an images integrity is its output, be it web or print. The problem with resolution is that it acts like human hair, you can always cut it off, but you can't add it on. This is where vectors come in. Remember that stupid french-curve on your protractor that didn't seem to be good for anything? The real name of that curve is the Bezier (bez-e-ay) Curve named after a french mathematician. The beauty is in the simplicity. Bezier discovered that you could create any curve using only two points. AI was designed originally as map-making software completly based on the french curve. Why is this important? Because vectors are resolution independent. The mathamatical relationship between to points will be the same no matter how far apart the two points are. This makes Illustrator a very powerful tool for artists since you can prepare artwork for every medium at the same time. The same image used to print business cards can be blown up for a billboard with no loss in quality. While AI is ideal for making clean edges and specific dimesions, it cannot edit on the per/pixel level. This is where photoshop comes in. Photoshop started as an attempt to simulate any process a professional photographer might perform in the dark room. This then gave way to simulated painting techniques making photoshop much more of an eisel than a drafting table. In fact that is a good way to think of it. Illustrator is a geometry calculator where Photoshop is a fresh canvas. A true digital artist uses a combination of the two to insure the highest image integrity during output. A photo prepared and color corrected in PS placed inside AI where text is added is a good example.