All righty, let's take a scientific approach to this debate:
My reference sources will be: The Original Star Wars Trilogy (No expanded universe sources), and situations seen in Freespace, along with freespace information drawn from the tech room. I'll be drawing on Dr. Curtis Saxton's work on the Star Wars Technical commentaries for some of the math (once again, ignoring any references to the Expanded Universe) and on the Freespace Wiki for information on GTVA equipment.
Speed: The fastest fighter in Freespace, the Horus, can reach a speed of 170 m/s using full afterburners. The X-Wing in the Star Wars original trilogy has been clocked using frame evidence at a speed roughly 290 m/s (Independant research on the part of the SWC design team by timing known distances versus the time the X-Wing takes to travel through them, i.e., over the hull of a ship.) In A New Hope, Rebel X-Wings are shown racing down the Death Star Trench at full speed, yet the Imperial TIE Fighters are able to overtake them. This suggests that TIE Fighters are therefore even faster than the X-Wing.
The Millenium Falcon has also been clocked by our team at around 260 m/s. A Star Destroyer in Empire Strikes Back is able to keep pace with the Falcon, suggesting that it possesses a similar speed rating. Comparably, the Aeolus has a maximum speed of 30 m/s, with most Freespace Capital ships falling short of that.
Edge: The Imperial Navy.
Strategic Maneuverability: Freespace ships posess Jump Drives, allowing them to travel great distances at great speed. Star Wars ships posess Hyperspace capability, which is very similar. Unfortunately the individual travel times can not be compared in these two, given the rather fuzzy timescale used by both sources. The GTVA, however, have an additional limitation that the Imperial Navy do not have to worry about: To travel between systems the GTVA must use jumpgates. This allows the Imperial navy greater flexibility to conduct attacks or redeploy forces at will.
Edge: The Imperial Navy.
Armour: For a comparison of these two, we must look to a common baseline, some attack which exists in both sources: Asteroids. The GTVA's destroyers are shown able to withstand impacts by several asteroids. An Imperial Star Destroyer's Bridge tower is struck by an asteroid of similar size, though greater speed, and is destroyed. This suggests that the hull armour of the GTVA's ships is greater than that of a Star Destroyer, though debatably considering the Asteroid seen in Star Wars had a greater kinetic energy.
Edge: The GTVA
Weaponry: The same comparison can be made of weaponry between the two universes, using Asteroids as a baseline. The GTVA's weaponry is successful in destroying asteroids, each blast from a GTVA Blob turret can vaporize small asteroids, or break apart larger ones. In the Scene in the Empire Strikes Back, the Imperial Turbolasers of all sizes, including the smaller point defence guns, are capable of vaporizing all sizes of Asteroid, suggesting a greater weaponry output. to quote Curtis Saxton, "we can estimate a lower limit on the power of each of the small anti-fighter point-defence cannons as between 250TW and 2000TW. The sixty-four visibly large dorsal heavy cannons must have considerably greater power than even this lower limit." 1 Kiloton of TNT is equal to 4.2 TJ of energy, giving the rating of the Star Destroyer's smaller guns at between 59.5 and 476.2 Kilotons of TNT.
As posted earlier in this thread, we are given numbers on one of the Freespace warheads which we can use to compare, the little more than 1 Megaton Harbringer. If the Star Destroyer's smaller guns are capable of delivering between 1/16th and nearly half this energy, with no ammunition restraint, the larger guns must be significantly more powerful than this, and thus able to stand on an even footing with the Harbringer, given their much higher rate of fire (at least once per second) and inability to be intercepted mid-flight. Their lack of ammunition dependancy puts each of these weapons in a more useful light, and given that each Star Destroyer (Avenger type, as seen in ESB and ROTJ) carries at least 64 of the larger class guns visibly, but most likely more of this class or a slightly smaller class are placed around the destroyer as well. The Executor, a ship twelve times longer than an Imperial Star Destroyer with a volume of hundreds times greater, must reasonably carry a much greater number of weapons of at least this damage class, if not much greater.
As mentioned earlier, however, the GTVA's beam weaponry may be able to pierce through the imperial shields, the Empire's primary defensive mechanism, but the much higher damage of the imperial weapons, and more numerous placement, must easily dwarf this ability, given that GTVA capital ships are not equipped with shields.
Edge: The Imperial Navy.
Shields: As seen in the battle during ROTJ, Capital ships in Star Wars are able to blast away at eachother for a long period of time, no less than one hour of constant bombardment between the two fleets. This suggests that, given the above stated weapon power, the Empire's shielding technology must be much greater than that of the GTVA, given their ability to shield their larger craft and withstand bombardment of that type for such extended periods of time. In fact, in the battle in Return of the Jedi, during this time only one Imperial Star Destroyer is seen succumbing to destruction at this heavy bombardment.
While GTVA Beam weapons may be able to pierce the Imperial shields, not all GTVA weaponry is of this type. In fact, Beam Turrets only exist on GTVA capitol ships (thus rendering Fighter attack relatively useless against the might of the Imperial shielding) with the largest of GTVA ships, the Colossus, having only 23 of these weapons. This means that the bulk of attack against the Imperial fleet must be conducted by large capitol ships, even though through Freespace 1 and 2 it seems the preferred method of attack by the GTVA seems to be sending in Starfighter Squadrons using physical warheads, the GTVA would need to send in its capital ships equipped with beam weaponry to overcome the imperial shield defences. These would likely succumb quickly to imperial bombardment, given the Star Destroyer's ability to deal damage equivalent to between 4 and 32 Harbringer attacks per second using only its large barbette mounted guns.
Edge: The Imperial Navy
Fighters: The Imperial Navy's fighters, for the most part, are unshielded, and would succumb quickly to GTVA weaponry, however, as stated, the Imperial fighters are much, much faster than their GTVA counterparts, and given the above stated calculations, would have a higher damage output than the GTVA's weaponry. If the Imperial TIE Fighters and the even faster Interceptors could use their speed effectively, combined with their much greater numbers (with each Star Destroyer carrying 64 of these) they could quickly overcome the GTVA's fighter defences, and focus on disabling the Beam Weaponry of the GTVA Capital ships, minimzing damage to their own.
Edge: The Imperial Navy
Given these evidences, the Imperial Navy seems to be able to quickly dominate an evenly numbered GTVA fleet, but given the stated size of the Imperial Navy, in the category of Dozens, if not Hundreds, of thousands of capital ships, they could smash the meager GTVA defences efficiently.
Oh, and Star Wars has better music.
