Primo is correct that it has a different pinout so it requires rewiring, just a few pin changes.
I doubt it sounds any different than the ECC82 equivalent or mostly equivalent 12AU7.
The 6350 was designed for digital computer use, not analog, which means the tube must cope with long periods of time spent in cutoff (digital logic is either on or off) and must have a more robust cathode to avoid failure because of the cutoff issue.
Leaving a tube in cutoff, i.e. heater hot but B+ not flowing, causes electrochemistry at the cathode where the cathode's silicon activator reacts with the alkali metals to form orthosilicates, creating an interface layer which ruins the tube. So the computer tubes were designed to active with less silicon. Some silicon was always required, because the alkali metals are pyrophoric in air (burst into flame), so the alkali carbonate was used when the tube was assembled (in air) and the carbonate was then reduced (in vacuum) using the silicon. The silicon also replenishes the alkali surface as the tube ages.
Tektronix used such tubes in the front-end of its oscilloscopes for similar reasons.