I've seen a lot of speculation recently that the exploration-focused Enterprise would wither under the might of a military-focused cruiser like a Star Destroyer. Is there any truth to this?
Absolutely not. The armament and defenses of Imperial Navy vessels are several orders of magnitude stronger than any Federation vessels.
While the main reactor output of the USS Enterprise is not listed, the shield force rating is 473,000 MW per generator. That translates to 4.73x10^11 W. The Enterprise is equipped with fifteen of these generators, for a total force rating of 7.1x10^12 W.
The Imperial I-class Star Destroyer is powered by an I-a2b solar ionization reactor. Peak power output is estimated to be around 7.73x10^24 W.
Even assuming 1% of the output from the reactor is dedicated to weapons, that's roughly 8x10^22 W devoted to the weapons systems. Let's assume terrible efficiency of 1%, that's 8x10^20 W impacting the shields of the USS Enterprise. Even with these abysmal efficiency numbers, a single salvo from the Star Destroyer exceeds the shield force rating of the Enterprise by 10^10 W. The Enterprise doesn't stand a chance.
The specifications for the USS Enterprise can be found here, and the specifications for the Imperial I-class Star Destroyer can be found here.
Yes.
While in many ways the technology in the Galactic Empire was centuries ahead of Starfleet, they were missing one vital piece of technology, namely transporters. While the defensive and offensive systems of an Imperial Star Destroyer far outmatch those of a Starfleet Galaxy-class vessel, a sufficiently motivated Starfleet captain in a situation in which no alternative exists could simply beam a few hundred photon torpedoes onto a Star Destroyer, disabling it's weapons, propulsion, and deflector shields. If the crew of the Enterprise acted quickly enough, it could stand up to a Star Destroyer.
[It's worth noting, though, that while we're having fun with the April fools' gag, questions should be about history from within the context of that universe/fandom. Given that this compares entirely different fictional universes, this might be better suited for /r/whowouldwin]
I can help here. Any time the Enterprise is outgunned, outclassed, outmanned or outwitted, they always come up with some bullshit solution involving nonsensical science and/or telepathy.