ORIGINAL: John
The main reason I said Vegas is more powerful is it is as it comes out of the box. Premiere is no where near as powerful out of the box. Yes with addons it is very powerful. But 999 for After Effects plus 799 for Premiere will get more tools then in Vegas but is that the question the OP asked? Then one would probably add third party addons. Premiere is a fine program but to me its way over priced and is lacking many of the tools that come standard in Vegas. However its up to the end user to decide but one must be fair when comparing the two apps. BTW Vegas can have addons too.
I'd have to disagree that Vegas is more powerful "out of the box". What specific features are you talking about? I think there is some confusion. For the money Vegas is a full featured powerful video editing application but I have never found it to be more powerful than Premier as a stand alone application in any regards, but rather the other way around. Premier just happens to integrate well with some of Adobes other products and that's a plus.
As far as After Effects is concerned, it is not meant to be a video editing application, but rather a motion graphics application. You would never edit a full lenth movie in After Effects. After Effects renders previews to RAM and is meant for short clip editing, like mike_mccue stated. Think of After Effects like an effects bin on steroids. Great for working with 2D graphics as far as motion, compositing, keying, motion in a 3D space, special effects, etc. However, that being said, RAM is large and cheap now a days so it's not impossible.