Iron Man vs Batman
Thor vs Wonder Woman
Captain America vs Aquaman
Spider Man vs The Flash
Hulk vs Superman
Doctor Strange vs Shazam
Hawkeye vs Green Arrow
Black Widow vs Black Canary
Vision vs Martian Manhunter
Green Lantern vs Scarlet Witch
Well, answering this with regards to the comics is very difficult as characters' powers and fighting skills vary tremendously with who's writing.
As for film versions, well a lot of these characters we haven't seen yet.
Anyway:
Batman v Iron Man : depends if Tony is on or off his game. If neither of them has an armoured suit, well Batman obviously. If Tony has a suit and Batman has prepped, well probably Batman. If they both have suits then Batman. If Tony has an IM suit and Batman has had no prep time, probably Tony just for sheer power.
Captain America v Aquaman. Depends if it's on dry land or at sea. At sea, gotta be Aquaman. Otherwise MCU Cap is super strong and tough, and if he has his shield probably sufficiently so to go toe to toe with Aquaman, although could he knocked him out ?
Spider-Man v Flash: well vs TV Flash, definitely Flash although Spidey would win the first half of the fight, but after a pep talk Barry would overwhelm him with some crazy speed stunt. Movie Flash ? From the trailers probably Flash, just based on his reaction time. Plus the current Spider-Man is very inexperienced and fallible. However the most likely outcome is that they would bond over science stuff.
Why not Flash v Quicksilver ? Flash v MCu Quicksilver, possibly Flash, but vs X-Men Quicksilver, different story !
Hulk v Superman: Given that DCEU Superman was able to break another Kryptonian's neck, Superman. If he used his heat vision and flight to his advantage Superman should easily defeat Hulk. However, if he just went toe to toe with MCU Hulk he'd get pretty beat up in the process.
Dr Strange vs Shazam: MCU Strange, with the eye of Agomotto, pretty much beats anyone as he can alter time. Otherwise his spells seem a bit limited, but we'll see what he can do in his next appearance.
Kind of a weird match up.
Hawkeye v Green Arrow would be very close, but tv Green Arrow is a badass who kills when he needs to and has been to hell and back. Going to go with Arrow just on how tough he is - comic book versions, I go with Hawkeye.
Black Widow v Black Canary , there have been several CW Canaries. Widow would have a huge advantage in fighting skills against the current Canary, but the sonic scream might take her out. The best contest would be Widow vs Sarah Lance, hand to hand only, as they're both killers - might give Widow a slight edge there, but give them swords or sticks and Sarah wins .
Vision v Martian Manhunter: well given that MCU Vision just about killed a team mate in his most recent battle, I be very nervous to be on his side. While in the comics Manhunter's mind powers, cunning and intellect might give him the edge, his fire weakness is a major liability. MCU Vision has an infinity stone in his head, and if he used any of its potential I think he'd obliterate MM pretty fast.
Green Lantern v Scarlet Witch: Given GL's super willpower could he resist SW's mind attacks ?
In terms of raw power GL wins ( even the Ryan Reynolds version) vs MCU SW but if he fought like a jackass he'd get trashed - Sinestro vs Scarlet Witch , very different story, Sinestro easily. Comic book versions ? Well, some versions of SW can rewrite reality, nobody can beat that !
Saved the best for last
Thor v Wonder Woman
Okay in terms of fighting skills, Diana has the edge as she has finesse as well as power - Thor is a skilful fighter, but based on their film appearances Diana looks better, and faster.
MCU Thor also loses Mjolnir, which would have given him a couple of tactical advantages - although Diana would probably be worthy enough to wield it. Still, with Mjolnir I think it would be a very even contest.
No weapons ? A pretty even contest, although we don't know just how strong Thor is, and we've seen Diana lift an armoured vehicle. Give them weapons and it's Diana.
More likely scenario, Thor would use his goofy charms and they'd go out for a drink.
Okay , now for the most important battle, which set of characters is more fun ? Well so far MCU by miles, except for Diana, and possibly MCU Flash.
Justice League will have to do a lot to make these characters watchable, while MCU has already earned its legions of fans by making such enjoyable films.