It depends on if it's the prime timeline or alternate timeline K'Vort.
Prime would be a Cruiser BoP.
Alt would be a Battle Cruiser.
The Alt K'Vort is not the same as the Prime K'Vort.
How do you determine they are not the same given they used (somtimes literally) identical footage for both types of ships?
The K'vort was also referred to by Picard and Wesley as battlecruiser and as Bird of Prey by Riker in "Yesterday's Enterprise".