There are many possibilities for this to be occuring.
It may be that while the game plays alright on your PSX, the discs may have scratches that bother the laser in your PC's CD-ROM more than they do on the weaker PSX laser.
If this is the case, then any image your PC makes of the disc - unless possibly made at very low speed, will still come out flawed with the same skipping problems.
It could also be that you have been playing around with your settings a lot, tweaking the FPS as you said, and you may have inadvertantly changed somethings. Or it may be that for whatever reason, your system is not quite up to the task of emulating the movie playback / game for some reason.
It could also be buggy emulation itself. I haven't used a PSX emulator recently as I have always had problems getting them work work as well.. But in any case if you list what plugins and all the settings you have enabled, I'm sure someone who knows will be able to help you sort it out..
Make sure any "special" optimizations for the game are checked, I think I recall there being one or two somewhere in the graphics settings of popular GPU plugins. I can tell you from my most recent experience dealing with Rage Racer, that the game also ran too fast for me unless I capped the FPS at 60 or so.. and even then, the game was moving slower than it does on a real console as a result.. PSX emulation is still an uphill battle for a lot of games.
