I LOVE animating in After Effects and see very few advantages to Flash unless interactivity is involved. Even when there is, it's possible to create projects in AE and import them into Flash. Some of the greatest pros to AE, in my opinion...
Z-SPACE. After Effects allows you to position elements in 3-D space, opening huge animation possibilities (see the Simpsons Movie with the "swooping" crowd scenes...that's AE).
3-D LIGHTS. The subtle gradient in the text in that pulp fiction clip comes from 3-D lights on 3D text. Text capabilities in AE are thru the roof, too. i use lights a lot to add 3D quality or realistic, dynamic shadows to flat-color objects, especially text.
KEYFRAME CONTROL. no need to create a keyframe in your timeline...AE automatically creates a keyframe anytime a property is altered...beit scale, position, rotation, opacity, etc. the keyframes are also independent for each of these properties, whereas flash just has one set of keyframes for each layer...all in all the interface in AE is MUCH better for complex projects.
PARENTING. great for character animation...wrist bone connected to the arm bone, etc.
EXPRESSIONS. Similar to ActionScript, opens up a wealth of possibilities that I've barely scratched the surface of myself...including "wiggle" effect which automatically creates random changes in a property for super-realistic motion.
EFFECTS. many are cheesy but some are great, including virtually every image filter available in Photoshop.
So yeah...advantages to Flash? Vector illustration in-program and interactivity. But even with CS3, I still find the drawing tools in Flash to be extremely clunky. Anything more than simple vector graphics and I'm going to be working in Illustrator anyway, so I might as well use AE.
I strongly welcome any arguments for Flash...I stumbled on this site because I was looking for a good reason to use Flash—reading similar AE vs. Flash topics. its still an industry standard in many regards but I just can't make a good case for it.
btw feel free to check out my demo reel at
www.andydv.com which i did most of in AE...im a recent graphic design grad. shamless.