Between Microsoft's debut console and its current gen one, which do you think is/was better, and why?

Listen 8 people, OG halo, 2 xboxes, 2 tvs equals LEGENDARY

OG Xbox. It was at least an interesting console with an exclusive Shin Megami Tensei game. Otogi games. Panzer Dragoon Orta. Jet Set Radio Future and Shenmue II. I struggle to think of anyting really unique on XBO.

OG XBox had more games unique to it during its time IMO, so OG XBox.

Just by having achievements the X1 is better then the original X Box. But it also has a better controller, better first and third party game lineup games in all genres, better UI, better looking hardware especially the S and X model. Better online and media capabilities even though it used DVD's for its games the orginal Xbox didn't even let you play DVD movies on it without buying the remote for it. If the original XBox would have had better third party support it might would have been closer but the PS 2 had way better third party support. With zero good JRPG's even the Gamecube had better third party support since it had Skies of Arcadia and Tales of Symphonia plus it got Resident Evil 4, Resident Evil Zero and a great remake of the first Resident Evil game. Plus its has a great enhanced version of Metal Gear Solid.

Did you forget Phantom Dust and Shin Megami Tensei Nine exist? Innocent Tears. Phantasy Star Online. Metal Dungeon. Blackstone.

Also hard to count RE against Xbox when Nintendo paid for them to be exclusive.

You didn't list Crimson Skies.  Phantasy Star Online don't even list because xbox version you couldn't even play offline without live account.  Gamecube version was superior.

Well considering you can play (Improved Versions) of OG and 360 games on the One makes this debate kind of pointless.

You can play Wii games on the Wii U as well, yet a lot of folks would consider the Wii to be the superior system.

One could argue that the older system was better in its time or had a better original/exclusive lineup.

I see CS more as a shooter