Round 1
Clyde and Bonnie rush Battleship, ignoring Frigate. Clyde gets on top of it while Bonnie circles around, each producing blaster vollies that would be crippling if not for Battleship’s incredible 5 PDs.

The Clyde gets an outer back section blown off fairly quickly by the Frigate’s mega beams, then goes back into the fray with Battleship. Soon enough, Clyde is blown to smithereens.
During this time, all the other ships have lost no sections, barring one frontal ablative on Battleship. Still, even the Battleship’s formidable PD hasn’t been able to protect it’s exposed rear completely. Bonnie has taken it to under half health.

Still, we never find out what would happen in a Bonnie V. Frigate match, as frigate destroys Bonnie soon enough afterwards (Despite having a hard time hitting with its inaccurate mega beams).
Round 2

This time a more aggressive Bonnie and Clyde rush in to dispatch the front three ablative sections of the Battleship. Afterwards, however, history repeats itself. The Clyde loses its three sections more or less simultaneously, leaving the core stranded and quickly dead. Bonnie then experiences targeting troubles, frequently acquiring Frigate with one of its blasters while shooting battleship with the other.

It, too, dies quickly and without making a significant additional dent in Battleship.
Winner: Battleship + Frigate!