I had a chance to play Leviathans on the weekend. First off - it was a lot of fun and I can see myself buying into the system.
As for using a similar system for BT War Ships, I can imagine the system being translated - not too big of a stretch - but there might need to be a few tweaks. Every ship has a movement value and a turn number which is how many hexes must be moved forward before a facing change. Alternatively, a ship can spend all its movement to turn in place to any facing. That would be a bit strange in a space game. There was no concept of inertia/momentum which you might want in a space combat game. The base game we played was on a plane with no vertical axis; I don't recall if there were advanced rules to introduce elevation. The system has fighters but we didn't play with them so I can't say how well that could represent Aerospace Fighters.
Ships have 4 "sides" - Port, Starboard, Fore, Aft - and all firing arcs and damage distribution are against those. A ship "side" has 6 damage locations (crew, engines, weapons, etc.) except for the largest battleships which have 12 locations on Port and Starboard. Each location has its own armor rating and if the rolled damage striking a location exceeds the armor, the location is destroyed. As locations are destroyed, subsequent damage hitting that location can result in a roll against the internal structure value and, if exceeded, results in destruction. As more locations are lost, an increasing positive modifier is applied on the roll against internal structure. There is no tracking of internal damage beyond a steady erosion of the single internal structure value (every roll against internal structure reduces the remaining structure by 1).
Dice are all 12-sided but with varying number distributions on different colors. e.g. I think Green were effectively 1d4. You decide if an attack is a single gun or multiple guns (to improve penetration chances), choose the dice appropriate to the weapons being fired (each weapon has a color), add a die (or potentially two and choose the best of them) for the crew (again of the appropriate color), add one or two dice for the target's movement/size, add a 6-sided die for hit location and roll everything. Check total against target armor at the rolled hit location.
Between turns, crew can attempt repair rolls against locations that were taken out on earlier turns (but not the just completed one).
Different ships can have different equipment such as different mixes of guns, turrets (with larger firing arcs), guns that hit multiple locations at once, extra armor, crew quality, engine sizes, etc. The Japanese ships in particular had some unique equipment but thankfully Christian was running those.
And that's really it in a nutshell. It's a very streamlined, fun, and logical system.