I used Wookiepedia for the Star Wars side and Memory Alpha for the Star Trek side.
SPEED - FASTER THAN LIGHT
Star Wars ships are capable of traveling 120,000 light years in a matter of hours or days, depending on the quality of the Hyperdrive. The biggest restriction is that Star Wars ships travel along mapped routes, being dangerous to leave the Hyperspace "roads."
Star Trek ships, at Maximum warp (Warp 9.99), it would take 15 years of non stop travel to reach this distance. However, no ship can travel at top speed for longer than a few hours. The Borg's transwarp network, however, is far faster than anything in either universe, being capable of traveling upwards of 10,000 light years per minute. That would put a trip through the Star Wars galaxy at 2 hours.
WINNER: Star Wars, as these debates focus on the Federation technology.
SPEED - SUBLIGHT
Any starship battle will take place at relativistic speeds, making Sublight speed the most important. This is where Star Wars falls horribly behind. The fastest ships in Star Wars are capable of 0.1c (One tenth the speed of light). Being generous, you could put the fastest ship at 0.2c.
Star Trek ships, however, are significantly faster. Full Impulse for Voyager was 0.8c. Standard full impulse was given to mean 0.5c, and it has been mentioned in several episodes how ships could reach 0.95c (using a static warp shell to prevent time dilation).
WINNER: Star Trek by a parsec
SENSORS - GENERAL AND TACTICAL
Knowing where celestial objects and other ships are will be crucial in a large scale combat, and even in a one on one duel. Star Wars sensors have shown a distinct lack of range and depth. Examples of this are the inability to scan Hoth for life forms, or even knowing the Probe Droid was there before visual identification. Tactical sensors are also very limited. The ability to target a specific point on a ship was significantly difficult, primarily because even a 2 meter (6 foot) target was hard to hit. Nor were they capable of telling whether the Death Star II's shields were up or not.
Star Trek excels at both. Ship sensors are capable of tracking other vessels traveling in FTL, as well as a range of about 10 light years. Planets could be scanned, informing of what life was on the planet. Tactical sensors were easily able to target specific weak points once scanned.
WINNER: Star Trek walks away with this.
COMBAT - DEFENSES
Star Wars uses shielding that needs to be dropped to allow the torpedoes to exit the ship. They also have the option of using two different types of shields, which could increase shield longevity when faced with energy and explosive attacks.
Star Trek uses one type of shielding. The most recent form is the Regenerative shields that are able to return to recharge while active. Star Trek also has ablative armor, which appears to be the equal to the previous shielding in strength.
WINNER: See Which is Stronger/
COMBAT - WEAPONS
Star Wars primary weapons are Lasers, Turbo/Heavy Lasers, Ion Cannons, and Proton Torpedoes. It is important to note, that Star Wars laser weapons are not actually lasers. They use Tibanna Gas to create the weapon. That effectively makes it a Particle Weapon. This point is important, as Star Trek fans have often used quotes from episodes that note how weak laser weapons are. Ion Cannons are shown to be super effective, yet rarely shown in use.
Star Trek's primary weapons are Phasers, Pulse Phasers, Photon Torpedoes, and Quantum Torpedoes. Photon Torpedoes were replaced by Quantum Torpedoes, due to the later's superior explosive power. Phaser beams have been shown to have a great level of accuracy and allow a constant attack on a specific point of an enemy ship. Pulse Phasers are basically an energy form of a torpedo, just faster.
WINNER: See Which is Stronger.
WHICH IS STRONGER???
As already mentioned, the Tibanna Gas used in the lasers of Star Wars takes it out of the category of lasers, when using quotes from Star Trek.
Another point that is brought up is the power output of Star Wars weapons, especially compared to Star Trek weapons and Star Trek shield strength. However, this point is equally ineffective in comparison. To use a real world example, you can have a gun fire two bullets at an armored vest. One bullet is a hollow tip, and the other a full metal jacket. Everything else about the bullet is the same. The Hollow tip will break against the vest, while the full metal jacket will go right through it. That is because of the composition of the bullet.
There is a counter claim from Star Wars. Using the same analogy, Star Wars would be firing a 50 caliber hollow tip, while Star Trek could be firing .22 full metal jackets. The sheer amount of force behind the Star Wars lasers would obliterate the armor/shield. However, when we look in universe, we have multiple quotes where the ship was being hit with an energy significantly stronger than the shields were suppose to be able to handle. The biggest was Voyager being hit by 90 million terrajoules of energy, when the shield's output was only 2,202 MW. That's over 400 billion times stronger than the shields could handle. By the energy output claim, the ship should've been decimated. Instead, it only received a few system failures.
Some people attempt to get more detailed, looking at asteroids being destroyed or some other visual comparison. However, all of those are subjective.
As such, there really is no good way to compare the weapons. Nor is there any reason to say that they can't be effectively equal in abilities.
WINNER Star Trek gets a slight edge defensively, due to the Ablative Armor. However, that category is basically a tie.
Star Wars gets the slight edge offensively, due to the Ion Cannon. However, as those have been circumvented in Star Trek, this category is also an effective draw.
COMBAT - RANGE
Though it is very common in both universes for the range of the weapons to vary, even on the same ship using the same weapon, this category is one of the easiest, and most important. In Star Wars, the range of a Turbolaser is no more than 100,000 KM (though some argue it is only 100,000 meters, we will use the higher number).
In Star Trek, the range of the Phaser maxes out around 200,000 KM. Torpedoes would logically have about equal ranges.
WINNER: Star Trek by 62,137.1 miles
RESULTS
Star Trek wins a space battle hands down. Even if you would accept the arguments of the power of Star Trek and Star Wars weapons and shields, Star Wars still loses due to three indisputable areas that Star Trek dominates: Sensors, Sublight Speed, and Weapon Range.
With those three categories, the Star Trek ship would be capable of easily staying outside of the range of the Star Wars ships, while targeting the weakest points on their ships. Star Trek ships would be able to out maneuver any Star Wars ship until it is destroyed or runs away.