In first scenerio they are locked up in a Greco Roman style match. The first to throw the other person 3 times wins. Supes can't fly or use flight to his advantage. They have to lock arms around each other in Greco Roman wrestling and that lock can't be broken or you lose points.
In the second scenerio they just stand in front of each other and punch the other until someone is KO'd. They alternate punches until someone is KO'd. The scenerio goes to durablity and striking power.
First scenario:
Greco-Roman wrestling is perfect for Darkseid's body type. He should beat Supes.
Second Scenario: I'm tempted to say Darkseid takes this as well but Post Crisis DS's main advantages over Superman is his versatility and his OE not his physical strength though I'd still say he edges Superman out if only by a little bit. When Superman saw Darkseid was hurt in H/P he couldn't believe it, that's how powerful DS was.
__________________
“Where the longleaf pines are whispering
to him who loved them so.
Where the faint murmurs now dwindling
echo o’er tide and shore."
-A Grave Epitaph in Santa Rosa County, Florida; I wish I could remember the man's name.
darksied wins both, in my opinion he slightly edges supes out in durability, and strength. although i am tempted to say with superspeed supes may win wrestling