Every Mafia story needs to be well told and well written.
Mafia 2 does this brilliantly.
Fuck sandbox. I don't need to be able to do crazy little side missions to appreciate the aesthetics of a truly brilliant and fairly original Mafia storyline. If anything, they would ruin it. They would side-track you from the story and the progression. We didn't care about linearity 10 years ago. Why the f*** should we care about it now?
Even a sandbox game such a GTA4 or SR2 restricts you at the start. There are certain places you can't go, weapons you can't obtain. However, in Mafia 2, you have complete access to every part of the map and every store from the start of Chapter 2. Halfway through, you have the ability to bust up a cop, steal his gun and go on a rampage. On Hard difficulty, I ended that chapter with a Thompson, Shotgun and 2 Handguns. Also, by the end of the same chapter, one is able to steal any car in the game world and both store and modify them.
The only downside is how aprubtly the story ended, although there is more than a slim chance DLC will fix that.