You are right in that Firewire was designed to use as little CPU power as possible. In fact, with Firewire, you can even hook up 2 devices directly without needing a computer to mediate the communications. This is not possible with regular USB (they later introduced USB-on-the-go to do something similar).
That being said, there are 2 issues:
How fast is the hard drive. Capturing live video from a DV Camera is fine, but the hard drive will be a bottleneck. The higher the RPMs, the better.
Second, are you simply capturing the raw video or are you running it through some algorithm (compress to Xvid, etc.)? If you are just capturing raw video, no problem. If you are running it through another program, then the faster the CPU, the better.
There should be no quality difference, except during playback, and only because the components in the computers are different. However, the actual video files will be the same quality.