I have a 1.6 ghz G5 tower and a 1.5ghz g4 powerbook. I also recently sold a 800mhz g3 ibook. The tower has 1 gig ram, the powerbook has 512 ram and the ibook had 640 ram. Running a few relatively low mem apps (say mail.app, safari and ichat), the three perform pretty similarly. The slower processor machines had fraction of second longer pauses between typical actions because of the difference in processor, but there are no "hang-ups" or beachballs. Now if I open another app, say iphoto, on each of these comps and I am switching between all 4 apps relatively regularly, the powerbook, despite the fact that has twice the clock speed of the ibook, will start to feel slower than the other 2 machines. Some actions it is still faster, but the long HD swapping hangups on the powerbook take a second or two. That is painful compared the fraction of a second difference in what i'm doing w/ the processor.
Most normal apps these days AREN'T PROCESSOR INTENSIVE. Only pro level apps like photoshop, and hardcore gaming apps will make a difference in processor speed noticeable. Even a game will be more dependent on the quality of the video card than the processor. This is why I always recommend to all my PC and Mac buying friends that they give up the processor bumps in exchange for RAM upgrades.
As long as you aren't running iphoto with 5,000 photos, 512 RAM should minimize the beach balls. A 1.25 ghz g4 is a solid processor, but the 4200rpm HD in the mini exacerbates the problem when there is a shortage of ram.
That being said, OS X performs well in a different way than XP. The overall GUI is a little prettier and a little laggier, but the multi tasking capabilities of OS X make switching from app to app a dream. Right now I am typing at work on a 1ghz celeron processor w/ XP. If a leave a web page open background for 10+ minutes and then i try to bring back to the front, the machine lags for several seconds while it rerenders the website. In OS X it would be instantaneous.
In conclusion, upgrade your ram and, unless you have defective hardware, your problem will disappear.