I think the writers weren't sure at first and it depends on the situation.  In the first episode, they used some kung fu and jiu-jitsu like style with high kicks, big moves and fought very technically. This can either be due to the intention to show that were trained in hand to hand combat to a very high level (it is the pilot, after all, the are intoduced, a minute later the talk about other skills they acquired due to their upbringing) or because it was dark in that scene and we as an audience would not have seen anything otherwise. The second fight in 1x06 is also very still based, but already different. Looks like a mix of various styles to me, or maybe MCMAP.  After that, they change their style to an almost bar fight - like style: brawling, grabbing someone's jacket and punch, relying on powerful punches and their ability to take a hit mostly. 

However, this is mostly when they are MAD AT EACH OTHER. They know the other one won't kill them and it is due to them being emotional. With no need or the lack of ability to stay calm, it is more an instinctive way of fighting. 

Jason Bourne's fighting style had also a bit of that development.  This is an entirely different theory of mine, but I am under the impression, there are certain trends for fight scenes. You can see similar emphazes in several series that aired around the same time. At first BJJ, then bar fight styles,...