Caroline,
I’ve experienced great results with 550D (aka T2i) footage (same compression as the 5D) and marginal results. The great results have come when I’ve transferred the footage on import in FCP with Pro Res or AIC. When I bring in the native/original H.264 QT file to a PC I get results like what you have described above. I know this doesn’t answer your question but hopefully it helps point in a more promising direction.
Best,
Jeremy Steel