I wouldn't recommend playing this "Definitive" Edition.

It adds nothing new to the game, it could have add things they have deleted back then. You know, side missions, melee weapons, elevated railway transport etc.

No, instead they added:
"Enhanced" textures - but not all of them of course so it could contrast badly
Glitches that weren't present even in the original game
And let me tell you that the new eyes will give you nightmares - after destroying some of the important expressions in the game

I wanted to like it - just because Steam gave the DE to me free because I own the original one and they also added all DLCs to it.
But I still can't. The DLCs bring nothing new to the story - except for a beginning of the Joe Adventures wohoo!
And those are the big ones - the small DLCs are classic 2010s bullsh*t. They give you some clothes that doesn't even match the setting and the tone of the game. The DLC cars are so OP that you dont need to search after any other car - or money because you can sell them for a large amount of dollars.
Yes this has nothing to do with "DE" and its also problem in the original game - except for a one thing - maybe you like the look of the dlc outfits or you want to really ride those cars - well guess what, in DE you have to wait for a certain missions so you can unlock them, hell, you have to complete the game for Veteran and Vegas pack!

The reason why I am so upset is that I found bugs that I never came over in the original - even the game breaking ones.
Their so called "stunning HD details" are nothing than imerssion-breaking textures that lost its atmosphere. I am not going to talk about the eyes because they are just horrific.

It's sad, with entire remaking of the first Mafia game, I thought that they will atleast add something that they couldn't back then or atleast repair some audio stuff etc.
No, its worser in every way. I really can't think of anything that I like more here than in the original one.

If you don't own it, don't buy it. If you own it - don't play it.
Instead try the original one, it's the masterpiece of game story-telling, even with "outdated graphics" :).