It is interesting to note that the version of the Negh'Var we currently have ingame is the one from "All Good Things", where the ship was referred to as "Attack Cruiser" by Governor Worf.
The script referred to that ship as "Voodieh" class.
It was actually quite maneuverable in that episode, similar to the Negh'Var in STO yet quite unlike the Negh'Var from DS9.
The version from DS9 is completely missing and I'd like to add that the (probably-slightly-less-than-soft-canon) "Starships" module of the Decipher RPG suggests that that version is not really maneuverable.
Which would fit what we saw in "Way of the Warrior".
So my propoasl would be to use the term "Heavy Attack Cruiser" for the Negh'Var version we have ingame right now to fit "All Good Things" yet keep the Negh'var differentiated from the Vor'cha terminologywise.
I'm also hoping that one day we'll get the Negh'var incarnation from "Way of the Warrior", but as a seperate ship similar to the way the Galaxy and Galaxy-X are closely related cousins.
For that one perhaps "Negh'Var Heavy Battlecruiser" or a simple "Negh'Var Battleship" would be fitting.
And that Negh'var could have a spinal lance type thing like the "siege disruptors" it fired at DS9 when they tried to talk to them.
I'm liking where this thread's going though, I also agree that everything being a battle cruiser seems strange, they carried battleship level weaponry, but only cruiser level armour so they could kill anything that could catch them and run from anything that could outfight them, the Royal Navy lost moe ships than it ought to have at Jutland partly because battle cruisers were put in the line of battle toe to toe with battleships, and that's not the role they were designed for.
I'd say the Vor'cha was a battlecruiser, and the Negh'var a battleship, if we went by the strictly naval classifications, they have the same weaponry essentially, but one is more agile and one is tougher.