I love PowerPC Macs, and the G5 Quad is the "best of the best" PowerPC macs, at least in terms of raw computing power.
With that said, in terms of useability your 2012 Mac Mini is a better computer in pretty much every way. The only thing the Quad really trumps it in is the fact that it can take two internal hard drives and can take expansion cards(if you need that ability). You can work around both of these on your Mini by the fact that it has Thunderbolt, and there are fast external hard drives as well as PCIe enclosures that work on the Thunderbolt ports. An external SSD in a Thunderbolt enclosure is likely going to be faster than any internal drive in the Quad, as they are limited to SATA 1 speeds.
The Quad is "stuck" at OS X 10.5(Leopard). The "mainstream" browsers, including Safari and Firefox, dropped support for PowerPC a long time ago, so if you want a modern, up to date browser and secure browser you have to go with something like Tenfourfox or Leopard Webkit. Both of these are great(and free) products that have a lot of free labor going into them to keep them viable, but still have their issues. There is also Flash, which stopped being developed for PowerPC a few versions ago, and has known security issues when used on PowerPC computers now.
It's also financially not a very good trade. Around here, G5 Quads are generally under $200. I'd expect that a Mini as new as yours would still be $400+.
There's a lot to like about the Quad, but I think you're getting the short end of the deal in trading your Mini for it.
