Best Practices- .MOV vs .F4V

Guys-
Could really use your help and advise. My Environment is all CS-4)
I've done plenty of AE projects in the past where I eventually use AE's RENDER settings to output either FLV or F4V. From there I simply leverage an FVP-PLAYBACK component to show the movie from within a Web Page.
This is my first project with HD (1280x720). I have imported some HD footage into AE after using Handbrake to convert m2ts to m4v(mp4). I did this because of CS4 AE challenges with HD Video imported directly. My desired output is still 1280x720. If I RENDER to a .MOV from within AE, FLASH will not allow me to import the .MOV file either through Actionscript-3 OR File->Import OR FLVPLAYBACK source. That one has me baffled. I tried some test .mov files I pulled down off the internet, and they work fine, so there's something in the AE render settings that Flash doesn't like.
I tried compressions settings of HDV 720p, Photo JPEG, and Animation. Flash won't import any of them.

If I RENDER in AE to a F4V then it works fine, but quality is not as good.

Last question is this :
If I RENDER to a .MOV format, then use Media Encoder to change to F4V format, is that preferred over using AE's RENDER to go to F4V in the first place?