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H.264 is a codec and doesn’t care whether its a .mov or a an mp4. Qucktime takes longer to process H264s than other programs (I find Adobe Encoder slower than QT) but neither are as fast as FFmpg. And all of these will be faster than AE. Many Mp4s out there are just .mov’s in an mp4 wrapper (as are FLV’s)
The output quality has to do with the settings you choose in your compression software not the compressor you used or the format it ends up in. H264 is a standard, not some variable thing that is reliant on what program made it.
Remus has a habit of saying “stay away from this or that” without having in-depth knowledge of the thing he is warning you about. If you are getting poor quality compresses, it just means your settings in your encoding software need to be tweaked. Its also possible you are asking too much of the codec. A most mostly black movie will be very small in mb, but a mostly noisy movie (lots of action and color) will never be super small if you want a clean, small mb movie in H264.
The issue is that AE can’t wind up through the content and look at all the frames before it begins encoding (Ok it can, but you are basically rendering twice). Any good encoding software can do a dual pass and analyze the content to get the best out of it.
.Mov is a perfectly valid clean format to work with and if you are on the Mac, one of the best choices if you want to keep file sizes reasonable. .Mov is just a receptacle for codecs. I can make a .mov in BlackMagic or Animation/best or Cineon – it’s still a .mov.
But your pipeline should be be: render out of AE in an uncompressed or Lossless format, and then put that final file through and encoder or QT or FFmpg or MS Expression or whatever to compress it.
Besides, what if there is an error in your movie that you have to correct in AE (wrong color, popping keyframe etc) do you really want to waste time encoding before you have a chance to inspect it?