Make sure CR is turned on in AE. Flash converted to a movie rasterizes the vectors because there are no vectors in movies. AE produces amazing animations if you learn how to use it but poor workflow and improper rendering techniques can foul up anything. You should have perfect results in AE if you are using the right techniques.
ALSO, and this is important, You can't judge video by looking at a still frame. You have to judge the quality when the video is playing at speed on the device it is intended to be shown on. Something that looks great on a computer screen may look horrible on TV or when projected. There is an awful lot technical stuff that you must be familiar with to produce good video for distribution on multiple devices.
Thank you Rick. I turned on CR for all the layers. I'm going to post a screen grab of what I'm talking about. I exported both videos in the same compression and both were made for HD 1080p in their settings. I exported the AE in animation codec to get the best quality. Here are the screen grabs from the exported videos in Quicktime. I would love to be able to have as crisp a picture in AE because I think I may be able to do more with it in the long run and it's more of a film industry standard.
If anyone can direct me as to what I'm doing wrong it would be greatly appreciated, but I think you can see the difference I'm talking about and why the Flash image is more desirable.
Screenshots of your composition settings, render settings, and output module settings would help.