My old Eximius-class could easily out manoeuvre that gigantic whale, and with multiple pulse cannon shots to the dorsal shields, and then 8 quantum torpedoes to the bridge she'd be out of the match!
Alternatively I'd go for her engines or just hit the ventral shields and fire quantum torps at her warpcore, she'd never be able to turn in time to take my ship out.
Still even with the Excalliber's size and lack of manoeuvrability, she's still pretty impressive.
Personally, at least in the Kobayashi Maru mod, I found the Excalibur's sensors were the most vulnerable thing. They had ridiculously low health, and there's a blind spot where only one weak phaser can hit you that gives you a perfect shot at them. Anything that can get through the ventral shields can take out the sensors with a photon torpedo, and the AI basically just gives up and wanders around while you slowly disassemble the ship from there.
Actually, I believe there was a version of the Constitution they made that was kind of a step between the original TOS Constitution and the Motion Picture revamp that the designers dubbed the EXCALIBUR class.
Never seen on screen, it was just something the modellers came up with, so it wouldn't be canon, but it seems to me it would be far more canon than that hideous monstrosity.
Actually, the modellers never came up with that idea. They just brought to life the concept art of the Phase II Enterprise, which evolved to the Consitution Refit.