This is would be an interesting battle between two great warriors who know how to use a sword, so let’s get right to it.

Jon Snow from Game of Thrones, has a sword is made of Valyrian steel. This is the top notch steel you can find in the Seven Kingdoms. It’s very valuable due to the fact that the art of forging a sword like this was lost hundreds of years ago. Weapons such as the Longclaw are moved down through generations. Swords forged from Valyrian steel are extremely sharp and well-built, but also not real heavy. It’s distinguished by its rippled design that can be viewed on the blade. It’s not unlike a Damascus Steel sword, which has the identical atypical qualities.

On the opposite side of the battle is Worf's Klingon Bat'Leth. Like the Longclaw, it too has been passed down through the generations. It’s made of baakonite, which’s a composite metal alloy, but also contains elements that’re ancient and, therefore, would be hard to get today. The folding mastery that was used by Worf's ancestors makes it an exceedingly powerful weapon with an edge that’ll stay sharp for decades.

The next thing to take into consideration is where the battle would be fought. Would it be fought on the bridge of the USS Enterprise-D or in the courtyard of Castle Black? Location will be key here.

You see, if it’s held in the bitter temperatures of the Northern boundary of the Seven Kingdoms, then the question becomes, does Jon Snow have the upper hand over his Klingon opponent? As Worf's home planet, Qo'noS, has a jarring territory susceptible to radical stretches between cold and warm weather, he may not blink an eye at doing combat in snow and ice.

Jon Snow on the other hand, might be unsettled when glancing at the depths of space from the large view screen that’s located on the bridge, or the climate control temperature that would most likely be too warm for him and drain his stamina as he was doing combat.

Both are vicious warriors in their own ways, but which one of them truly has the stronger desire to triumph over the other?

Worf was born into primarily the parallel of a royal house in Klingon civilization and then, orphaned at an early age. He was then brought up by humans in an adequate farm environment and then he made his return back to his home planet. There, he would make his official declaration of becoming a warrior. Because he was "tarnished" by his human adopted parents, he wasn't really given the red carpet by Klingon society. Eventually, he became the first Klingon to join and graduate from Starfleet Academy. From there, he’d quickly rise through the ranks of Starfleet.

Jon Snow was also pretty much born into a royal house, except, being illegitimate, he wasn't precisely a full member. He was brought up with the family, but his sole option of a future was to be shipped off to the ‘Wall’ where he’d live his whole life as a warrior and nothing else. Life at Castle Black was most certainly rough, being that it was in an isolated and grim place, where most of the occupants were lawbreakers and society failures.

So, who’d attempt to validate themselves greatly in battle, the shunned orphan or the bastard son?

I think the weapons are basically evenly matched, so they’d cancel each other out as far as advantage goes. As troubling as being in outer space could be for Jon Snow, I believe the affects would probably be minor when it came to fighting his opponent. Again, they were exposed to unfavorable family surroundings and were primed as warriors, so I think they’re equals in those regards. What it comes down to is age and experience.