I treat the game like a little trip down memory lane, obviously it's not going to be anything special by today's standards.
The world is amazing but empty, just like before. Not really different from Mafia 2. They could've expanded it but they didn't. The entire focus is on the story and the city is just a very atmospheric backdrop, a bit of a missed opportunity. They said there would be new side missions but AFAIK, there aren't.
The game does indeed feel wooden at times, the animations ate pretty bad, the shootouts aren't much better. One might even argue it's not worth the money for the content. Even though I haven't paid full price, it still cost me more than some other games that are much richer in this regard.
Still, I just wanted to reexperience one of my favourite games with better graphics and I think I'll get my money's worth just driving around the city and completing the story again.