I was thinking last night that the TOS movies never showed an even-match battle between the Enterprise refit/Ent-A and any other adversary.
TMP - overwhelming adversary
TWOK - Khan sucker punched the Enterprise and probably wouldn't have if they had their shields up.
TSFS - Enterprise was damaged and couldn't compete with a small Bird of Prey
TVH - no battles
TFF - take by surprise by a Bird of Prey at the center of the galaxy
TUC - surrenders to a D-7A, sneak attacked by a cloaked Bird of Prey
Only the D7-A would have been an even match for a heavy cruiser such as the Enterprise. The Enterprise outguns a Bird of Prey 10-to-1 according to Kruge in The Search for Spock.