My 1.25 GHz PowerBook G4 feels as fast or faster than my older PC, a well balanced and tuned 2.4 GHz P4. But aside from games, most of what I do (DV editing, 3 and 5 MPixel home photos, presentations, web surfing, email, word processing, light desktop publishing) would be doing just as well on a 1 GHz G4 or a 1.8 GHz P4. Just as long as I had 512 MB of RAM. All of the bundled applications run as great as can be, as have the others I have purchased for it.
I would say that aside from the DV -> MPEG2 transcoding times, you'll find the 1.25 GHz G4 to be far fast enough for just about every task except for the newest games. And in that case, the 32 MB Radeon 9200 will be the limiting factor anyway.
If you want to compare the Mac Mini to a similar sized PC, such as the powered Nanode (Nano-ITX) system, you'll find that the G4 is over 2x faster than than the Nanode's 1.0 or 1.3 GHz Via CPU. Plus the Mac Mini has a real GPU and dedicated gfx ram, not shared onboard graphics.
There is, of course, a "differentness" to Mac OS X. Just as there was back in 1988 when people were comparing NeXTSTEP (Mac OS X"s ancestor) to traditional Unix systems of the day. It was a very different OS with a very different structure and a very different GUI. Many of the idea pioneered by NeXTSTEP have found their way into Windows and Linux over the years, and the OS itself was greatly overhauled during the Rhapsody/MacOSX project. Some elements were borrowed from "Classic" Mac OS 9 to further add to its varied background. Ever tried going from a Mazda to an Alfa? That's sort of what its to go from Windows to Mac OS X. It's a very different world.