“…because PNG keeps all the quality of the EPS.”
That is 99.9% incorrect.
PNGs are bitmap files and EPS are vector. You may be able to get a good PNG out of an EPS, but it will be a conversion. You need to understand your graphic files before asserting such incorrect info.
I would recommend converting the EPS to Photoshop layers at a very high resolution (600 – 1200dpi) and importing those [layers] into FCP. FCP takes advantage of the additional resolution when zooming in and out and stuff. For example, I scanned a business card at 1200dpi, and did a motion animation that zoomed in on one letter, then panned across the words… the texture of the paper showed at that zoom and everything was crystal clear — unlike zooming in on a 72dpi graphic. Try it!