This is a difficult one. I enjoyed every gen you listed (even those before) but Ill have to go with:
DVD Generation (6th): The BIG Daddy (ps2)
-Suikoden 3/4/5
-Xenosaga's
-All things Shin Megami
-Rogue Galaxy
-Summoner 2
-FFX
-Playing all my wonderful ps1 games
Xbox
-Armed and Dangerous (this game had the best weapon EVER in video games...the shark GUN!)
-KOTOR's
My favorite game of all time does not fit into this category, but overall this was my favorite. Its Crystalis on the NES, for completeness sake of course.