I have played both and I love both. As far as gameplay goes, Battlefield 4 is more of a standard FPS, just on a large map with vehicles and toppling buildings and such. Arma 3 is a military simulation which takes place on one of two maps. The first is 1 square kilometer, the second is 270. Arma 3 is the most realistic war game out there. However, I think its fair to say that they are both great games and it just comes down to which style of play you like better.
As far as graphics, Arma has some very nice looking scenery but I think Battlefield wins by a bit.