mpeg2 is not mentioned for editing, it is a muxxed stream of audio and video signals.
when you scrub thru your file, the recompressor has to redefine the picture, cause mpeg2 compresses the way, that only the information of the differences between two frames is saved. so, when you go ahead 52 frames, the players misses the infos of frame 51, 50, 49... depending of the compression, there are key-frames with the whole information of a single frame every XXX frame (e.g. every 500th frame=20sec with 25fps).
there's no difference between qt pro, FCE or pro - they all use teh qt-engine.
editing such streams needs a recompression into an editable file format, e.g. .dv-stream - in tresult, you got every single frame in its whole beauty - and BIG files...