I feel like I should answer your question, but I can't get over the idea that you're collecting last generation's H/W now. It's not old enough to be nostalgic- it's not new enough to be current.

But I think I can say this- there were very few xbox exclusives that would be worth playing today. You mentioned Halo and both of those play on the 360 through backwards compatibility, so I wouldn't get a xbox(1) just for them. Other exclusives have sequels/remakes on the new systems (Fable, for instance) so I wouldn't worry terribly about the,

Xbox(1) was a heavier-duty machine that the PS2, so games tended to run/look better on it vs the Sony box... but if you're playing 10 year old consoles, I don't suppose you'd really care about the difference.