The first system you listed just isn't going to cut it.
The second system should run it as long as HLSL is turned off and nothing else is running in the background.
It still might have sound skips here and there, but not many.
Running multiple monitors can also be the difference between it running full speed or not.
IIRC Ridge Racer runs on the same MAME driver. I can run that full speed on my my 3.9Ghz i7 laptop, but it chokes if I'm using both the laptop screen and the HDTV output. If I turn off the laptop screen, it runs fine.
A lot of people end up just settling for the PS1 version.