Round 1: superman vs Thor (standard versions) Batman vs moon knight Green arrow vs hawkeye Round 2: all star superman vs rune king Thor Batman vs hawkeye Green arrow vs moon knight
Round 1: superman vs Thor (standard versions)
Not even going to weigh in on this one. I've done this dance too many times already.
Batman vs moon knight
Batman is far more skilled and usually has better gear. Marc doesn't have any powers currently, either, at least as of the last time I read anything with him in it.
Green arrow vs hawkeye
Hawkeye should take Current Arrow. Better gear and a lot more feats.
Round 2: all star superman vs rune king Thor
Where do people get the idea that All-Star Superman is so impressive? He's really not even better than normal Pre-52 Superman. RKT absolutely stomps him.
Batman vs hawkeye
I don't see Bruce struggling with Clint's arrows, and there's no doubt who wins once Batman gets close.
Green arrow vs moon knight
Probably Green Arrow as long as Slayton doesn't have his carbonadium armor. Ollie wouldn't do too poorly in h2h, either.
Marc Spector has had a few different armors, several of which would give Bats pause. As far as skill goes, I don't see Bats as being more skilled. Smarter overall because of how the writers made him, however Marc is willing to do whatever he needs to to take down his enemy.
The one big problem with Bats is more hurting him than helping is the fact they just piled on the knowledge of every Earthly martial art plus several alien ones just to try and make him a super kung fu guy, but has still been beaten by Azrael, Cassandra, and Ithink a ninja too.
Basically, they made him a jack-of-all-trades. Marc knows a handful of fighting styles and perfected them over years of practice and use. And they did a better job of explaining how and when he was taught as opposed to just knowing it all. It's more subtle things like that that actually make me enjoy Moon Knight a bit more than Batman.
There was also the fact Bruce inherited billions of dollars and could just get whatever he wanted. Marc Spector had to work for it as a mercenary and soldier of fortune, going to every grimy and blood filled corner of the world doing the jobs and missions nobody else can or wants to do.
Marc made millions on his own accomplishments, and when he finally snapped out of his "hate the world" mentality when he 'died' in Egypt, he invested that money to build a company and become the agent of Khonshu, aka Moon Knight. Not for the sake of justice, but as a means of atonement for all the horrible things he'd done and will probably yet do. Which is just another factor fitting into his multiple personalities.
Bruce and Marc are almost complete opposites in how they do things. Bruce is smart, a detective and has super-computers to help him figure things out. Marc has connections and people he sees and visits in order to get the information he needs to figure out what's going on or to help stop something from going down.
One dresses in black, the other white. Both have dodged bullets. But the difference is, Bats is almost entirely about stealth and sneaking up on you to avoid taking the first shot. With Moony, he can be just as stealthy, but he wears white not to hide, but to say that it doesn't matter if you can see him, you still can't hit him with your gun. Both of them know how to inspire fear in criminals. Though Moony did a better job with the dread.
I think another difference is Bats is trained how to avoid taking a hit as much as possible and counter. Moony knows how to take a hit and make you suffer for it. Even taking a slash from Taskmaster's sword, whom became increasingly more terrified of Moon Knight. It's one thing to make them afraid, it's another to make them cry when you're the one bleeding.