Based on the comments in the battle of the week and the 'size of fight in the dog' discussion, I thought this would be an interesting topic.
In general, I think Captain Marvel (Billy) would have performed almost exactly like Superman did in the fight with Death of Superman, up to the very end, where he would have been unconscious, and Doomsday would still be alive, but in bad enough shape that almost any relatively powerful guy could finish him.
It goes to the 'size of the fight in the dog', as this was Superman's ultimate Rocky Balboa moment, and I don't think Billy has the level of mental toughness Superman does....I think he could have fought about as well, but at the end of the day, Supes willpower had DD dead and left him dying.
Oddly enough, going down easier might mean that Marvel would have survived...
How would Cap Magical lihnting do on DD, and think that in the end, Cap's restrainst and lack of killing mode has him beaten down and killed off...
NOW how would BA, someone a spowerful as Supes/Cap, but much more ruthless, had fared?