What do you need the app to do? Figure out your content (Simple graphics, complex effects or shot footage? Decide now.) and delivery (DVD or web or both? Decide now.) method before picking the app. Get signoff on storyboards before you commit to an app.
But here’s some more info:
1) Not everything in AE will make a practically-sized SWF file. Look in the Help under SWF to see which features will have to be rasterized and will give you a large SWF file.
2) AE is good for video. If your delivery is DVD or web video, you should be fine with AE. Why would it be better than Flash for video? You can make fancy effects with blurs, 3D and stuff that Flash cannot do.
3) If it’s a toss-up, use whichever app you know better.
4) I’ll have to assume that you know AE and Flash well enough to weigh their pros and cons, but you just don’t know what this job needs yet. As I wrote, you should nail that down first, with storyboards, before you pick the app that will execute those storyboards.
If you need more info, please feel free to write back.