I have played both, both deserve praise in their own way:
Mafia II is very story-driven, amazing graphics, linear and short gameplay.
Just Cause 2 is a very good looking sandbox type game, a very large world, where you can spend a LOT of hours doing the craziest things, almost everything you can think of, besides the game's own missions.
I recommend you watch some gameplay of both on Youtube, and decide which style suits you. Both are strongly recommended.
Edit: and since you mentioned "pick one" as I am into sandbox games right now, go with Just Cause 2.
Both are good games and i liked Mafia 2 better than just cause2 because of the story and graphics as told above by "Eldd". The setting of the old era was the most appealing thing with old classic songs and radio talks going on when you ride out with your classic cars.
Just cause 2 in beginning looked like fun but later it got boring with no story at all and the side missions were not so good.
So from my side it will be Mafia 2...Go for it mate!!!!!!!!!!
Mafia II for me. I've played both and would prefer Mafia II over JC2 because I personally liked the graphics much more appealing in it. Just Cause 2 for me looked very cartoon-ish and just didn't get me hooked onto it as much as Mafia II did.
Also, I really loved GAT4 and since Mafia II is in the same genre, it worked out for me. I loved exploring the open world in Mafia II. Plus, it's set in the 50
s so the classic feel to the whole gameplay was a nice change. Good story too, better than GTA4.
Again, these are all personal views and like the poster above stated, try looking up some vids on youtube, etc.
2 votes for Just Cause 2 and 3 votes for Mafia II.
I liked both games. Just Cause 2 with all it's stunts, exploring, easter eggs and don't forget the mods. The mods are the best part of the game. Story wise, it isn't really that appealing. But the graphics comes to your attention really quick. It's really an open world, sandbox game.
Mafia 2 on the other hand, you can't explore much at all. It's like the GTA series, only that it's really lacking some exploring elements. You can buy clothes (main thing I liked about it). Money didn't even matter as there wasn't much to do at all. The gameplay and graphics (especially the character deatils) are extremely good. The cover system is all in all good without much problems at all. The story is well made too. Although, the game didn't seem much challenging at low difficulties.
The car driving in both games is something that I disliked though.
On short, my vote is to Mafia II.
You should definitely try Just Cause 2 as well. Maybe you should play it after Mafia 2.