Gamera brings up most of the points I was going to. Save one.
The real problem with this "versus" is that it pitches a late-war, near-last-ditch design against a considered, incrementally-tested, and combat product improved one.
Even the limitation to "AP only" is flawed. By the time the Tiger II went to the field, the Germans had no tungsten for penetrators; they were down top solid steel shot. Even the AP for the 105mm M1 gun used a 50mm penetrator rod in a discarding sabot. Which would punch through even Tiger II frontal armor with ease.
There's a tiny bit of room for argument if we limit the rounds to HE only, no HESH ,HEAT or the like. Which limited us to the 105 L7/M68 gun, as I do not believe there is an HE round other than the HEAT round in 120mm.
The Abrams uses spaced armor specifically designed to face anything the Soviets had, right down to T34/85, so the M1 is not likely to ever need reactive armor, except for rear-echelon unite in 3 or 4 decades (if they emulate the M-48A3s),
If we up this to a Hunting Tiger, that' evens things a bit. Other than suspension issues, track issues, drive train issues.
Now, for an interesting "versus" why not an Il-2 Sturmovik vs. an Abrams?