Apple never made a G5 mini. Not even a prototype that anyone outside Apple's secret labs would be aware of. The G5 processors and cooling modules were larger than the whole mini itself.
As for Cube vs. mini... if you plan on using the machine for anything more than basic web, email, word processing, get a mini.
To make a Cube reasonably useful on OS X 10.4 or 10.5, you'd need to upgrade the processor, RAM, hard drive and video card.
I put together a Cube project last year. Bought a G4 Cube off eBay and upgraded the processor to a 1.7GHz G4 (1MB L2), swapped the HD for a 7200 RPM 120GB unit, replaced the video card with a flashed GeForce 6200 (for Quartz Extreme support) and added 1GB of RAM. Also replaced the case with a PowerLogix mod for more air flow around all the upgrades, added a virtually silent base fan, a virtually silent GPU fan and moved the voltage module to a better ventilated area.
It runs 10.4 pretty well and 10.5 passably.
And even an Intel Core Solo mini would run rings around it.
The Cube has collector value, but that's about all. For actual use, a used Intel mini is a far, far better value. I'd never want to subject myself to trying to use a stock 500MHz, non-video accelerated Cube on OS X 10.4 or 10.5.