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Battle Tardis stealth prototype is one of the original prototype Battle Tardis that were first commissioned. It was upgraded to an experimental stealth model for the celestial intervention agency just before the last great time war. It sports dual twin cannon molecular disintigrators and 8 time torpedo bays, with a mark II gravity tractor and an aft mini singularity mine generator.
The time war mark II Battle Tardis sports dual twin molecular disintigator cannons, gravity tractor mark Ii, 8 time torpedo bays, a micro singularity mine generator and an Artron energy cannon.
With the MARK II, there were 500,000 created, and of the 500,000 MARK I production models, they were upgraded, to a certain extent to the MARK II production model, except, that in the MARK II, the engines were a Class 6B engine, while the MARK I upgrades still used a Class 6A. Some time lords who commanded the MARK I preferred the upgrades to their ships with the 6A over the Newer Mark II 6B engines, because the MARK I class 6A version was tried and true, whereas the Class 6B Engine was prone to faults, however it's power utilization curve was greatly reduced and provided a more efficient distribution to the weapons array. if you had the Mark I and got the upgrade to Mark II, the engine you have a 6A, would mean that during battle, there was some lag time as you would have to build up power between shots, and could leave you open to an attack.
When you see the Stealth colour recognition model, it is in reflective Black, (piano Black) and can reflect the stars when not cloaked, as it fired, making it still hard to see in space. In many ways, the upgrades done to the Prototype to create the Stealth were used by the time lord technicians, and the head technician called the Architect, to create the Mark II upgrades. So the Mark II, while still very different, has design similarities with the Stealth model.
All ships are accounted for at the end of the last great time war, except the stealth TARDIS from the Celestial Intervention Agency (C.I.A.) as it's whereabouts to this day are unknown, and can mask it's signature from any enemy and other TARDISes.