I would avoid outputting compressed from Moho. I usually see color shifts and other issues with it, especially with .mov.
If you want to output a movie file with its original quality, you'll need to use uncompressed or use a lossless codec, or choose PNG as your codec. That or output an image sequence using a format like PNG, and then compile the footage in another program with better options for compressed movies. (This second choice is what I do, even when I'm not rendering for compositing.)
If you're rendering for Vimeo or YouTube, there is another issue you may run into. Even if you render the movie file with perfect color and detail, you may notice a shift in the black levels after the file has been uploaded. If so, you need to adjust the levels for the movie. When I output my movie files for Vimeo or YouTube, I use Vegas Pro with a Levels effect applied at the project level. Inside the Levels effect there is a preset called Computer RGB To Studio RGB. The rendered result will look washed out when played locally but it will look correct after you upload the file to Vimeo or YT.
This adjustment can be reproduced in any video editor or compositing program with a levels filter or tool, but you should only apply it last and only for the 'online streaming' version of your movie.
For final output, I typically use Sony AVC, which is a variant of H264 in an .mp4 container. This is good for streaming like YouTube or Vimeo, and for playing on other computers. For delivery to a client, I usually render to ProRes 422 or higher, or DNxHD .mov files.
For my own editorial and archival footage, I've been using MagicYUV, which is a fast mathematically lossless codec, in .avi or .mov. After installing the codec, I can select it in Moho when I choose 'AVI for Windows' (as opposed to just 'AVI',) or 'Legacy QuickTime'. (FYI, .avi works better than .mov in Vegas but the .mov verson seems to work fine in Premiere.) I highly recommend MagicYUV. There is a free version but even the 'pro' version with high-end options is only $15 right now, and a real bargain.
TBH, I don't render movie files straight out of Moho. I generally find it faster and more reliable to output PNG image sequences, and then compile the frames elsewhere. This way, if Moho chokes in the middle of a big gnarly render, I only need to render the bad or missing frames, not an entire movie file again. Also, fewer resources are used to render an image sequence, which makes it easier and faster for Moho to finish the task.
Note: I'm running Moho on Windows but the movie options should be more or less the same in Moho for Mac. I think the Mac version may have better Quicktime options.