You should replay the original, it is still significantly better at game design and storytelling (and physics, believe it or not).
Remake is still fun and has gorgeous graphics, but it needlessly changed quite a few aspects for worse. A consequence of having different people in charge and also only having 2 years to make it.
Someone on youtube translated some of Daniel Vavra's comments about the remake:
"The worst part about the remake is that I had an idea I wanted to convey, but now the idea is gone and the only thing that remains is just a plain shooter game, just because someone rewrote the script, just because someone didn't put his own idea in it, just like "family is my everything, I would do anything for them" is a sentence you will hear from every guy when he drinks 5 beers, there's nothing more to this... If I was a script doctor, I would tell him to rewrite the whole thing, purely from the professional view, the original script from 18 years ago works better, if someone rewrote the script and didn't understand what the idea was, and ignored the biggest ideas from the first Mafia game, then I'm pretty sad and disappointed because all the effort and ideas we put in the first game are gone and this will be the only thing people will play in the next 10 years. (because of the better graphics) It's missed opportunity, it's pity that most of the magic is gone, don't get me wrong, the graphics are gorgeous, the acting is great, but the philosophy of the realistic game is gone, everything that made the game a classic is gone, now it's just generic third person cover shooter, and there has been lot of these games in the last 15 years. I put a lot of effort, time and a whole part of my life to make this game work, and trust me, it was a hell."