I have both moded.
I prefer the Xbox...
It simply got hacked like nothing else. You can ftp to it, you can map the drives on the Xbox on your PC, you can run games from the hard drive, you can run emulators at perfect speed
Well like Snes, Genesis, Nes etc...
Also with the same game on both consoles, the Xbox version will usually be the better port.
Now about backing up games it just takes more time. Since you must copy the game to HD, upload it to your PC HD and make an iso image if you want then burn it.
You can also send files directly from the Xbox DVD-Drive but it takes more time.
So for a Xbox game to be ready to burn takes 20-40 mins.
PS2 has some nice exclusive titles though. A good modchip is required to enjoy the PS2 like it's meant to.