*cough cough*...my money is on kirks ship...*cough cough*
This is something derived from an idea where it was the Enterprise hovering over a whaling ship near Alaska instead of the Brel Class Bird of Prey. But I decided to go with the Carrier Enterprise going up against the starship Enterprise. Needless to say the Constitution Refit would obliterate the carrier and pretty much the entire US fleet.
Think about it, SABO rounds and anti-ship cannons against energy shields, you wouldn't scratch the surface of destroying that thing.