I know how you feel Giorgio. Had the same experience. English isn't my native language and I didn't find the english dub bad at all. Of course back then it was revolutionary large for a game and was pretty good in general but since the standards got higher and higher it seems cheaper and cheaper. I think people tend to exaggerate when it comes to the voices. There are much MUCH worse dubs. Anyone, even those that don't have English as their native language can tell that the dub of Shenmue II is WAY worse and also why. The voice actors sound bored and unemotional as hell or way over the top to the point of just being silly.
I still really like the English dub of the first game. It really isn't bad. All the main voices are pretty good and pleasant to listen to. Some NPCs do sound awkward, they always did. The problem with the english dub lies more in the recording quality. They did a poor job there, the voices tend to be overly loud, to the point of clipping and it seems the recording studio was has a microphone in an regual ol' empty living room. There is such reverb in so many lines...
Then again, in Shenmue the Movie the voices sound really good. Much clearer, no clipping and no reverb. The dub just get's soooo much better with that quality.
The Japanese dub is generally of higher quality. The recordings are cleaner, without the issue and some lines are actually less compressed and sound WAY cleaner then anything in the English dub (in the game). The voices are also generally better, because they just had more know-how over there. Also it's really just so authenic, especially because the Americans speak broken Japanese with a lot of English inbetween.
There are some voices that don't sound so good here too, though. Master Chen for example has a very "throaty" voice that just sounds voice and annoying at the same time.