The only reason someone would pull out a knife or a gun in a fist fight is fear. The fear and adrenaline combined can make any lackey miss from a 1 metre range. A knife is accurate, you can slash with it and so forth. When it comes to knife fighting there are 2 types of it:
The one in the moves is where the person is an idiot and holds the knife in front of them out fear and not knowing how to use. They are basically giving away their wrist for you to crush.
The second style is the one where you should just run. I doubt any martial arts can save you from this. If they brandish a knife, take a step back and hold the knife close to their body, pointing at you, while the other hand is outstretched ready to jab at you, then they are an experience knife fighter. They will use the hand closest to you to distract. They could literally just wave it at you and the next thing you know is they are pumping the other hand holding the knife into your rib cage.
I think the real advantage to a knife is that it extends the reach and potentially damages in ways a punch alone would not. Fear, skill and adrenaline may give the attacker some advantages which is why retreat/avoidance are the best choice it you aren't adept at controlling the attackers knife arm.