I'm martially trained, so it would depend on whether I thought one person was going to be victimized by the other, as well as whether weapons were going to be involved. I would try to yell for other people to help break up the fight. If those weren't available, I would take out whoever I have to take out.
I have intervened on a guy I didn't even know, psychologically torturing some probable ex-girlfriend of his out in public one day. It wasn't to violence yet, but I wasn't going to let it go there. Little did I know I was not alone, turned out there were 5 construction workers watching the whole thing that were going to jump his ass too. What actually happened is first I got his focus on me, so she could escape. Then I threatened to call the cops on my cell phone. I figured this scumbag wouldn't like interaction with cops, as he was probably a felon.
One time I intervened on some guy who seemed like he was posturing to beat someone up. But I may have misread the situation, as the 'victim' seemed awfully surprised by my intervention, like Who the F is this guy? I waited from behind my car, so that I had some metal in the way and it was clear I had no intention of advancing towards them. I had bear spray ready, but for all they know I might have had a gun. Or he could have had a gun for all I know. He talked blah blah about how things could get 'complicated' here. I said there wasn't going to be anything 'complicated' about it. The situation ended, we went our separate ways, no fight actually happened.
Afterwards I considered the level of risk I had just taken, for someone that wasn't my problem and maybe wasn't going to get beat up anyways. I realized I had made a big mistake of judgement, taking it upon myself to "straighten someone out" about their public behavior. If I really thought there was a problem, I should have watched from afar and ratted them out to the cops, without them knowing I had anything to do with it.
One time in front of a food pantry, this 1 homeless guy was threatening to beat the crap out of this other guy. He was incoherent and enraged. I was in my car, and did my cop cell phone threat thing. The other guy wasn't having any of it, he was gonna beat this guy anyways! I was like, damn, this guy is stubborn, guess I'm really calling this time. Started dialing. Then the guy got a grip and left. Close one though. I really don't want to actually have to get the police. That creates resentment and someone could take vengeance on me for it later. It's better if the police are threatened and that causes people to break off and find something better to do.
I am not a coward though. I'd have to think there's a lot of personal danger to just let someone else take a beating.
One time I helped break up a fight between 2 knuckleheads on a dance floor in Las Vegas. One of the knuckleheads was so angry that then he wanted to start taking swings at me. But he was so pathetic that all I had to do was dance out of the way of him. He was like trying to throw punches at me from 5 feet away, guess what dude you can't hit anyone that far away. This lasted about 10 seconds and then these 2 BIG Samoan bouncers cleared the floor. We were all escorted out. I told them my story, that I wasn't involved and was just trying to keep people from getting hurt. They let me back in.
I have been warned that if you intervene in a marital spat, they can BOTH turn on you. So you really have to know how to watch your back, and have good judgment about what you're getting into.
I had some dorm mates next door in college get to some really scary emotional point where I thought there might be violence. I intervened, banging on the door. My reminder that there were other people around, and that human standards of behavior were in play, got them to break off whatever they were escalating towards. The guy was mortified, I think he realized how out of control he had just almost gotten. They were miserable but no violence came of it.