well yes and no. depends what you're doing.
there are path & mask tools in AE which can be used to create vector images, but most of the time you'll be animating vector images which have been created elsewhere.
with AE you can import illustrator files, psds, video footage, jpgs, targa sequences etc into the same composition.
so, most of the time you'll be creating artwork outside of After effects in photoshop, illustrator or whatever and bring it into AE to animate (rather than create it inside AE from scratch) It's a really powerful compositing soft
ware aswell.
think of after effects as a kind of animatable photoshop. it shares many features with PS, but you have a timeline.
to me things done in flash look like...well exactly that. like flash.
I actually prefer flash for drawing vector stuff, but thats mainly due to me hating illustrator.
I've used both flash and after effects quite a bit and find flash quite limiting in many ways.