Battle of Time

Dastan (Prince of Persia) w/ Sands of Time Knife weapon

vs

Cage (Edge of Tomorrow) w/ Mimic time ability

Cage gets sword

Dastan and Cage are fully trained up in their ability.

Cage can't lose here, he'll just reset every time he dies until he knows exactly how to counter Dastan's moves

Even though PoP can rewind immediately, every time Cage dies he'll start the fight over from the beginning with Dastan having no knowledge of the fight ever happening.

Ok second Battle

Cage

vs

Bill Murray (Ground Hog Day)

Both aware of there powers.

Both get knives.

Cage. Even though their powers are pretty damn similar, Cage has the advantage of being a trained soldier with actual combat experience. And he's in much better shape.

Yup, Cage has got this. The guy spent who knows how much time training and fighting in an active war zone against an advanced, hostile civilisation. Billy Murray taught himself how to play piano...

Stalemate in an endless cycle and while I see Cage killing Connors in the vast majority of their matches, eventually with enough matches the probability of Cage being hurt and bleeding out before he dies and losing his time-powers isn't zero, which would net Connors a win and end the cycle

Outcome: Endless stalemate with Connors having a chance of eventually winning due to probability