I'll go with the guy who can send me to the edge of creation and back. Where No One Has Gone Before really was a great episode that captured the imagination, one of Star Trek's finest. Too bad they got so bogged down in politics and other non-sense later on.
In general this whole thread kicks ass!! I quoted you specifically because I agree with you 100%
Where No One Has Gone Before to me, truly is the heart of Trek.
The Nth Degree feels on the same wavelength and is a great episode to capture that same wonder and imagination as
Where No One Has Gone Before did before it.
As already mentioned, Barclay was upgraded by the Cytherians to launch them into the centre of the galaxy for mutual sharing of information (And Picard had that throwaway line about how the newly shared data will take decades to study).
So this method of propulsion was purely technological, and feasible for a very advanced race, like the Cytherians (unofficially I think "God" in ST V is a Cytherian, perhaps a criminal imprisoned on that desert planet)
The Traveler on the other hand, is part of a species that is capable of using their thoughts to channel warp energy and enhance it. If I understand the concept correctly, they can take a warp bubble and exponentially increase its power to fold space to accelerate the velocity of travel of the object within it.
So there's still mathematics involved, which was Kosinski's specialty. He was basically inputting the equations, and the traveler was using the power of his thought to refine them further for him. He made a mistake and launched the whole ship to the edge of the universe, but at the cost of draining himself to the point of death.
Pure coincidence that this part of the universe allowed normal humans to use their thoughts in the same manner, although with far less control. Still they could add some force of their own thought to the Traveler so he could survive to show up another day.
So the Traveler warp was incredibly ludicrous speed, to the point that Picard even said "I believe there would be a warp speed that could take us to M33, but no amount of velocity (technologically speaking) could take us where we are now"
So yeah, Traveler warp billions of times faster than Barclay warp.
I doubt Q cares much for the Traveler. The Traveler is powerful by human standards, but still way below the evolutionary scale compared to Q.
Q could go to the edge of the universe and back all by himself as many times as he wants. Traveler needs a warp capable ship with very efficient warp engines and engineers skilled at the mathematics involved in creating that efficiency, AND it pretty much drains him to try it even once.
Off topic, I don't get the Wesley/Neelix hate.
Wesley's bad moments were due to bad writing, and even then I think only up to around 3rd season, then he gets phenomenally better.
Neelix was a good idea, but not implemented really well. Occasionally he rose above mediocrity, but for the most part I liked his character. I'm saddened that he never made it to the Alpha Quadrant.