This is purely subjective, as I know many who believe that Shenmue II is a better game.
I however love Shenmue I for many reasons. Primarily it’s the atmosphere.
There is a word in Norwegian I would explain it as, Koselig, but it doesn’t translate. But it feels more homely, yet exotic. And in my opinion a far more immersive experience.
It something to do with the setting, naturally, but also the pacing. It doesn’t feel like a game, but an experience. Where Shenmue II, feeling more like a game, if you know what I mean.
@BlueMue said it best really. Some very great points are the weather effects, they hands down made the atmosphere way better. Forklift driving was also a lot more fun than crate carrying!
Again, saying that one game is better than the other, is difficult. Its very subjective and both settings have their own strengths and unique feeling.
But for me, I think a lot of the nostalgia and atmosphere and feeling I get from Shenmue I, came from the time I played it too. I remember it was spring, and raining. I was just 14-15 at the time, and felt free! So that helped a lot
And to this day, I will get in to that feeling and want to play Shenmue in the spring/early summer when it rains or is grey outside.
Sadly, I know adult life will probably not give me the same feeling for Shenmue III.