I think the frame rate is a bit iffy on consoles too.
If you have a PC too, definitely get that version (IMO).
I let Mafia pass me by, it wasn't until a couple months after its initial release that a friend lent it to me, saying it was good.
What did I think of it? Well, I get bored of most games after getting only part way into them, but Mafia hooked me all the way through to the end, and after then I was playing the extra Free Roam Extreme mode.
A truly excellent game. Hoping for the sequel.......
You do get Free Roam modes so you can just drive around and mess around - limited at first, but you unlock more as you progress through the main story, although you won't get hundreds of side missions, stuff to collect, etc. like GTA. It is essentially a story led game and you're basically stuck with the missions it gives you. But that story and those missions are excellent, and if the theme interests you in the first place then you should be hooked all the way to the end.