I've got a PS2 and a XBox and they're both pretty good. I do prefer the PS2 joypad over the XBox one though.

The PS2 has been out a lot longer than the XBox and has a worse hardware spec because of this. I do agree if you're interested in graphics quality then get the XBox.

In terms of games, the PS2 is backwards compatible with the Playstation so you've got a bigger library of games to choose from.

If you want to hack it then get the XBox. It's pretty much a PC with most of the legacy bits removed and a special BIOS. You can replace the HD with something bigger and then load your games onto it if you wish.

If you want to program it with proper documentation then get the PS2 and the Linux kit. You'll get nearly all of the programming manuals for the PS2 and it'll let you do your own thing pretty much.

The XBox DVD dongle is just an IR remote receiver pretty much. The XBox itself is perfectly capable of playing DVDs but Microsoft decided to make it an optional feature.