Short answer: Alien queen if its unarmed combat 1 vs 1 and both are free to fight, cant see how the super predator would be able to kill a queen with its hands and even if it did the acid would melt/kill the predator.
IF armed: Whoever gets the drop on the other.
The alien queen if we watch aliens movie isnt really designed for combat, or moving around quickly, hell looked almost like she was struggling with walking around, and for being 4 and a half meter tall she didnt look that big compared to ripley in the power loader which is 2 and a half meter tall.... Seemed like the queen walked around squatting pretty much, else she would tower the power loader with ease.
Also, find it confusing at times in the movie where in the nest she seems huge and at when she gets out from the drop ship landing gear, but when put against the power loader and when ripley holds the queen above the god damn airlock: Seems pretty much as tall as a human? Guess the queen isnt that much bigger than a normal xenomorph and the egg sack isnt that huge either.
I liked the idea of making the queen alien as a egg layer and is worthless at moving and fighting, her body and legs isnt really designed for running around like a T-rex but is flimsy and when walking looks like its not built for it. Hence why she needs her xenomrophs to protect her.
I had to rewatch the Predator movie several times to judge how powerful the upgraded predator/super predator is(I hate how the movie is a big mess in editing and how dark everything is, hard to see what is going on in the scenes at times..) and came to this conclusion:
The super predator isnt bullet proof as some claim in this thread: Normal 9mm pistol rounds killed him off and injured it several times in the action scenes, and then I count shots to the head where earlier bullets bounced off.
A knife also injured it with ease. Various weapons did the same during the whole movie. But strangely in some scenes they gave it plot armour as an M4 with 5,56mm assault rifle didnt do any damage to the head in one scene but did later in the movie, seems its bullet proof depending on when the plot demands it.
Also its own blade and weapons could hurt it as well which I would presume other predators have as well.
The scene where the normal predators wristblades broke against the super predator: Was actually it hitting the armour or the hand computer thingy which from earlier movies is bullet prof. So the super predators skinn would been damaged/injured if the normal predator hit it anywhere else.
So alien queens tail would make short work of the super predator.
What it has going for it is that its stronger than a normal predator and has plasma casters and predator weapons so in a distance fight it would easily kill a alien queen.