[Shenmue]-----Yakuza-----L.A. Noire-----Sleeping Dogs-----[GTA Series]
The above model is a rough idea on how I think that games outside of both open world extremes (shenmue and gta) are related.
Yakuza is very much a spiritual successor, but nothing is quite like Shenmue in every single aspect since there are so many systems that I feel are pivotal and are not implemented in the above games (e.g. in game time is a huge one which definitely impacts gameplay and heightens the sense of immersion). Heavy Rain/Fahrenheit are worth mentioning though imo they don't quite fit in the above scale.
imo how you'll end up percieving the above games will greatly depend on what aspects of shenmue were your favourite. imo Yakuza is the closed in terms of gameplay, minutae in details and story and vibe. L.A. noire is closest in terms of scale, ambition, authenticity and well as some of the mechanics. Sleeping dogs means more so to GTA for sure, but it has a few nice nods and the location makes a nice change (I enjoyed this game despite not really liking gta type games, and it's the closest to shenmue alongside l.a. noire on xbox 360 for sure.)
I only recently got into Yakuza. I played about 1/3 into the first game years ago before stopping because I didn't really enjoy it, but I recently played the 3rd game and I much enjoy that one and the similarities are there.
Just note that for all above games, your enjoyment will largely depend on accepting that each game is very much standalone and going in and throughout expecting something shenmue-esque may likely leave you dissapointed, as it has with me. Instead, just appreciate it for the things that it accomplishes on its own or that even shenmue couldn't do, and you'll leave with something worthwhile :-)