This great image requires a t-shirt urgently. When I came across it today on Digg I thought: "I can't believe we haven't asked this question in Gizmodo yet. Hello?" Who would you think would win: an Imperial Star Destroyer or the USS Enterprise? And a simple answer won't work. You have give us actual technical arguments. You know, arguments like a Star Destroyer is X bigger and has Y amount more destruction power than the Enterprise. Or a couple of torpedoes can destroy the Star Destroyer bridge, then a third one will destroy it. Or a Star Destroyer can unleash a whole buttload of TIE fighters and Kirk would lose his shirt in a second, without meeting any sexy female alien. Note: In what could count as a time-space fabric-ripping event, I have to say that I had sex with someone once, after discussing exactly this. And she was a woman. Probably an alien. [Digg]
I think my User Avatar gives away who I think would win, but I think it comes down to 3 separate factors: Maneuverability, Technology, Commander in Charge.
First, The maneuverability of a Star Destroyer is nil at best. They are mainly used as an orbital platform to launch small fighter craft from (Tie Fighters, Gunboats, Lambda Class Shuttles, and the like) or to prevent smaller craft from getting through a blockade (ala The Empire Strikes Back). In close combat, they would be nearly useless. It's obvious from all the dogfights in the Star Wars saga that whereas the shields on a Star Destroyer deflect and absorb energy weapons from most smaller craft, their shields cannot defend against solid objects entering their range at high speed. For example, in Empire Strikes back when the Star Destroyers are navigating the Asteroid field in search of the Millennium Falcon, a small asteroid strikes one of the Star Destroyers' bridges and obviously there is some sort of catastrophic failure (as evidenced by the commander of that Star Destroyer's Holo-Image winking out during the conversation with Vader). Assuming they were at full deflector shield power, what is to prevent a photon torpedo, a quantum torpedo, or a kamikaze shuttle pilot at low warp from pummeling the nerve centers of the heavy cruisers. No star destroyer has enough maneuverability to avoid a sudden impact such as that. It makes you wonder why nobody sent a slew of proton torpedoes at the Bridge of a Star Destroyer. I guess no small, one manned fighter could get through the battery of turbo lasers to be of much use.
On the side of the Enterprise, it truly would depend on which class of ship we're talking about. Enterprises from Kirk's era up through Captain Rachel Garret's would have the advantage of being a smaller craft with infinitely more mobility than a Star Destroyer. But, lest the shields hold against the turbo lasers, the impulse engines (no doubt doing the majority of the thrust power for the federation ship) could quickly be completely destroyed, thus rendering the Enterprise dead in space. But let's save that for the next section. As for the Enterprise-D, it is possible that due to the largeness of the Saucer section will diminish it's mobility, and the Galaxy classes definitely have trouble surviving when in outright dogfights (for examples, see any of the episodes concerning ship to ship combat in the Dominion War episodes of Deep Space Nine), so the Star Destroyer may have an even match with that class of starship. As for Sovereign Class Vessels, those were truly designed with the Borg in mind (according to apocrypha of books and technical manuals), hence the more streamlined frame, the removal of civilians, and the increase in armament. I would think that a Sovereign class vessel could run circles around a Star Destroyer, as lithe as it is, and have no trouble out maneuvering the bulky battleship of a bygone era. As for the Enterprise-J (Aha, didn't think I'd bring this one up, did you?), I don't even think that the SD would hold a candle to it speed-wise.
In the meantime, the enterprise could also use a whole host of preprogrammed battle tactics (something that also factors into the third part of this scenario, the commander). Another example: Let's say that the sensor packets for a Star Destroyer ar rudimentary at best, something akin to a Battlestar's DRAIDIS array; It can tell where ships are at a point when they enter the array's detection. If the Enterprise were to use something such as the "Picard Maneuver" (the military tactic used at the Battle of Maxia, not Jean-Luc's signature uniform tug), the sensors on the Star Destroyer would register the Enterprise as half a system away rather than right on top of them after Dropping out of their FTL, and delivering a crippling blow to the Star Destroyer. There would be no way for the turbolaser batteries to re-align to compensate for the arrival of the Federation Ship at a much closer range, and probably much to late to scramble new fighters or recall the ones sent out to attack the starship when it was originally something deteted on long range sensors.
The next question is that of Technology (weapons or otherwise). It is a matter of record that Lasers (at least in the Star Trek form of weaponry) are outdated when it comes to Federation Shields. In the episode of TNG, Unification, Part I, Worf is almost incredulous that an attacking ship is using lasers to harm the Enterprise, and the same issue is raised when the Enterprise crew is tricked into fighting the Satarran's war with the Lysians. In that episode, when in a position to destroy the Lysian Central Command (which used lasers, by the way), Picard refused to destroy it on the basis that they Lysians base was severely underpowered for what the Federation Starship could match and that they didn't pose a threat to the Federation. So with that, it renders the use of Turbolasers vs. Federation Shields moot. On top of that, there is a high possibility that the Enterprise could cycle its shield frequency, thus even if constantly pummeled by all of a Star Destroyer's main batteries, that a switch of the frequency would make the Imperials melt their guns before making a dent.
Phasers on the other hand could be something that brings a Star Destroyer to it's knees. Phaser is the acronym for phased energy rectification which is the process of turning stored energy into an energy beam without intermediate transformation. Energetic plasma is pumped to a prefire chamber made out of a superconducting lithium-copper. There it undergoes a rapid nadion effect in which strong nuclear forces are liberated. A protonic charge forms and is released in pulses to the emitter made out of the same superconductive crystal. A beam of electromagnetic energy is released from it at the speed of light (definition courtesy of Memory-Alpha.org) The Enterprise (depending on which class of starship) has wnwere from 7 to 16 phaser banks ranging from Mark X to Mark XII, these all can be used in concert with strafing runs and independent targeting systems. Phasers can also be tuned to various frequencies to pass through shield harmonics and do damage to whatever is beneath them (i.e. when firing phasers at a Borg, Starfleet officers are only successful until the Borg adapt their personal shield harmonics). A full scan with advanced enough sensor packets could detemine the Imperial shield frequency and the phaser banks on a federation starship could cut through a Star Destroyer hull like a hot knife through butter.
Photon & Quantum torpedoes also would be something that the imperials may not be able to defend against. As shown before in countless episodes (an most notably in Star Trek First Contact), the enterprise can fire volleys of torpedoes on multiple spreads, all with independent tracking systems. There would be little chance of a star destroyer to take out all of them at once. An the specs on Quantum torpedoes make a strong case they they might even survive a full bore onslaught: The quantum warhead relies on rapid energy extraction from zero-point vacuum. This is established from an 11-dimensional space-time membrane, twisted into a Genus-1 topology string, housed inside the ultraclean vacuum of a 1.38 meter-long teardrop shaped zero-point field reaction chamber. The detonation of a photon torpedo warhead, enriched with fluoronetic vapor, inside the torpedo powers a continuum distortion emitter. It expands the membrane and pinches it out of the background vacuum. The membrane forms into subatomic particles accompanied by a high-explosive energy release. Packs quite a punch that a star destroyer may not be able to defend against.
Shields on a federation ship (even at the most basic deflector level) make the weaponry from imperials moot from their general specifications: In the event of combat, the navigation deflector performs as the very first stage of a starship's defenses - the deflector can deflect (or at least reduce the damage sustained of) most laser fire and primitive projectile weapons. And that's just the navigational deflector, full blow shields? No contest there.
Beyond the main weapon classifications that a federation starship is outfitted with, something tells me that the Empire Strikes Back already gave the Enterprise a decidedly non lethal way to cripple an Imperial Star Destroyer: Ion Beam from the deflector dish. The deflector dish's uses have been modified (an was made to be modified) several times through Star Trek history to emit certain pulses, beams, and wavelengths. A deflector dish is fully capable of emitting directed energy ion pulses, and if targeted correctly, will cause an imperial star destroyer to be dead in the water. The only downside to this solution is to emit a pulse of beam from the deflector causes heavy damage to the emitter and can only be used at sublight speeds.
Lastly (to wrap up this not so concise comment), the last piece in this puzzle would be the commanders of the various ships. If the Enterprise had a "tough as nails, willing to get anything done" commander on it, like a seasoned Cpat. Blackjack Harriman, or Picard (Post-Dominion war), something tells me that the Star Destroyer would be in trouble. Especially if there was just some mere peon in charge of the Destroyer (like say Admiral Ozzel or Piett).
But with someone like Grand Admiral Thrawn or Dalaa, their knowledge of tatics and ruthlessness may up the chances for the Imperial's survival. This would be the only main point of contention that I could see when comparing the two ships. In the end, some of this comes down to the fact that the Empire is a military organization not known for it's mercy vs. how far a Federation ship will go to defend itself.
All in all, I think I've made some rather convincing arguments for StarFleet's Flagship, but am still left to truly wonder who would triumph in this situation...