I at least hope this blog can be a reference to Black Adam vs Superman, to see how they're written and what actually happened whenever they fight.

Black Adam and Superman had two fights in comics, the first in DC Comics Presents #49 (1982) which was Pre-Crisis, but in that same story arc he fought Superman and Captain Marvel at the same time, which is pretty bad-ass, the next was in Action Comics #831 (2005) was a more drawn out fight. Either way, in my opinion these fights do not get much mention, so I decided to give some mention.

DC Comics Presents #49 (1982)

I should note that the Shazam characters were designated Earth S whereas the Silver Age/Bronze Age Superman was designated Earth One, regardless Black Adam is on Earth One to which he is already causing mayhem, in this case he is throwing around cars which immediately catches Superman's attention.

After Adam realises he is on Earth One, and explains to Superman how he realised this, it cuts to a fight, to which surprisingly Superman attacks first.

The fight is going back and fourth, yet they are described as evenly matched and that the fight could go on for days. By Superman's own admission, Adam still stands well after Superman's best blow.

Superman seemingly surrenders, but that's not the end of it, as he spies on Adam holding the Billy Batson of Earth One in his grip. However, that's not the Superman we know and he quickly returns.

Long story short: Shazam does not work for the Billy Batson of Earth One (at the time, Captain Marvel/Billy Batson was Earth S so this was another version, the one on Superman's Earth), Captain Marvel is technically a separate entity but Adam then goes on to fight Superman and Captain Marvel at the same time, but is outsmarted and thus defeated.

Gallery

Next fight...

Action Comics #831 (2005)

This is the only Post-Crisis fight they had. Superman is a bit hot-headed in this issue and holding back less due to characterization, he is suspicious that Adam has ties with super-villains. He approaches Adam once he spots him.

Next, it seems like Superman is getting ticked off at the mere sight of Black Adam...

And...Adam lands the first punch, which rocks Superman hard, by his own admission he hits harder than Captain Marvel, surprisingly Adam does not really seem as angry as many see him other stories.

Superman is sent down but comes right back at him, he lands a hard punch on Adam's chest yet he states on-panel he is not holding back (probably is due to mental blocks).

The fight's not over yet...

The brawl ensues, tearing apart some of the ground.

It ensues further with Adam pleading innocence, until of course Adam's carelessness nearly leaves an innocent dead.

Luckily Superman saves her.

Honestly, Superman seems the aggressor in this fight (which is odd....considering this is Black Adam after all).

And then Superman launches a punch - whether it could have busted a Moon, I don't know but it seems odd considering 81 billion ton force should surely kill innocent people around...

And the fight ends.