Hello, Rodi

Actually Premiere isn´t a compositing software but a video editing one. AfterEffects is a somewhat of an industry standard (much like Photoshop), and it´s by far the most common compositing package at the moment. It´s from Adobe (More info available here)
Combustion is Discreet´s most available (and less pricey)compositing package. It has a somewhat steep learning curve (Specially if you´re an adept to Adobe´s Products) but essentialy they both do the same. They composite. You just have to learn how to, and in reality it won´t differ too much whichever one you should choose. You´ll have to learn how to use them anyway.

By the way, now that you asked, Premiere is used to actually edit video, and it´s being used like crazy to make all those anime music videos you can find around P2P networks.

Prices?
Premiere goes for 549 US$
AfterEffects goes for 699 US$
Combustion goes for 4995 US$

Hope this helps ...