My ranking was always thus:
Speed: Star Wars, Star Trek, Traveller
Communications: Star Wars, Star Trek, Traveller
Shields: Traveller (black globes, anyway), Star Trek, Star Wars
Weapons: Complicated: Traveller has meson guns, which are likely the best beams, while Star Trek's torpedoes have FTL capabilities. Star Wars fans point out the Death Star, but there was never more than one of those bad boys at a time.
Tactical: Star Trek, tie between Star Wars and Traveller. Star Trek ships have cloaking devices, they have transporters, and are shown to be very capable of adapting. Three times during the show there were instances of our heroes deciding to just cause stellar flare that were capable of wiping out multiple ships in seconds. A small Klingon fighter used that tactic to destroy an entire shipyard.
Matchups
Traveller vs. Star Trek: In a ship-to-ship fight the Traveller vessel would lose every time. Star Trek ships are capable of real-time FTL operations and could stay out of range as they pleased. Things might end up stalemating if the Traveller ship had sufficient point-defense to withstand the torpedo volleys.
In a fleet-on-fleet combat things would be trickier. I still favor Star Trek here, provided the Traveller fleet can't catch the Star Trek fleet in a pincer and hammer away with mesons.
Matching any empire from Star Trek against any empire from Traveller is once again a no-contest win for Star Trek simply because of their superior speed of travel and communications, at least initially. The Travellers seem to have much larger empires, and might have enough ships to cause a problem, but unless they all attacked as one, there would be little chance of their victory.
Traveller vs. Star Wars: Ship to ship, I've got to go with Traveller. Mesons penetrate shields, both ships are going to fight at similar speeds, since Star Wars vessels can't navigate beyond lightspeed and fight at the same time.
Fleet vs. fleet is a different game, because we have to assume one Death Star II (at least if it's the Galactic Empire we're considering) per fleet. That thing can make mincemeat of a capital fleet, but since most Traveller fleets have small-craft sections, this might just be a draw. Enough of a defensive screen to get a single meson into range and you'll start seeing heavy losses for the Empire.
Empire vs. Empire probably goes to Star Wars, by virtue of their speed and communications.
Star Wars vs. Star Trek: one-on-one, it's no contest in Star Trek's favor. Their ships warp as they please and can simply engage star destroyers from behind.
Fleet vs. fleet is pretty much the same thing. The Death Star isn't going to hit anything once the first ship or two falls to it's weapon. If we're talking Klingons or Romulans, they'll just sneak right in and do their business while the Empire has its pants down.
Empire vs. Empire is more evenly matched. The Empire is probably much bigger than the Federation. Even though some sources claim a million planets for the Empire, there's no way that Dooku's separatists would have been considered a threat in Episodes II and III if the Republic was that large. Unlike Traveller, the ships from Star Wars can marshall their forces to pretty much anywhere. They're hampered by the fact that they can't blindly navigate like warp drive can. You have to scout "hyperspace routes". By this logic I'd say that neither show could invade the other show's territory successfully.
