I bought my classic Xbox for myself. At that time, DVD players were like $250. For just another $50, you could get a DVD player that played video games. Hard to justify not buying an Xbox! The PS2 could play DVDs too, but the only way to control the DVD player was with the controller. Xbox, on the other hand, offered a remote and a sensor that plugged into one of the controller ports.
Of course, the Thompson drives they put in those early machines were total shit. Mine won't recognize a DVD at all anymore, and it takes a while for it to recognize Xbox games. But since it's like 8 years old, I guess that's to be expected.