I'm not sure which box Ty played his game on (Hugebox, hah good one), but I bought the UK/PAL release, which was JPN-dubbed with Engrish subtitles, so I had the fortune of not hearing Sega-of-America-English dialogue.
Obvious things, graphics were noticeably better (texturing, character animations, map size, architecture, # of characters on-screen), music was better with nicer action/mystery-oriented themes given the Hong Kong setting (instead of being flat-out boring or irritating like the Hazuki Household), no English dubbing, no talking to people with your eyes 99% shut as if Ryo fell asleep standing up.
Gameplay/Adventuring. Story pacing was much MUCH better in my bloated-Kung-Fu-fighting-asian-movie-loving opinion. Shenmue II's (DC) Disc 1 has more action than all of Shenmue I. Fights are thankfully more frequent. Fighting mechanics and controls feel faster and more fluid, more responsive. Greater variety of character/fighting styles as well (it IS Hong Kong, afterall). QTE's are more frequent, way more EXCITING, tho the button combos are kinda insane. Increases the overall coolness factor. Adventuring/Investigation was streamlined in such a way that I don't remember any searches being so rediculously ambiguous as "looking for sailors." The pacing tries to make sure you're not stuck in an on-foot search for "too long." Acquiring cash is easier (thanks to gambling), no silly full-time jobs, and job mechanics are simpler in comparison. Puzzles are not as obscure as those in Resident Evil(s). Finding your way around and getting help from townsfolk isn't difficult. Ryo even has a wonderul "Stalker/Rape mode" view (I'm kidding, yet not. There is such a lock-on auto-follow mode).
I find the story/events more interesting, characters are more interesting (not "questionable" like Fuku-san was). Main character interactions are more frequent. Xiu Ying is HOT, and the Chun-Li fortune-teller chick is SO CUTE.
That's it in a nutshell. You don't have to believe me.