Aside from the fact that tubes starting with 6 indicate a 6V heater supply and tubes starting with 12 indicate a 12V heater supply, and are NOT interchangeable, there are more issues.
In the same family of tubes such as dual triode 12AT7, 12AX7, and 12AU7 there are significant gain differences.
In a given circuit using overall loop feedback, using a tube with less gain that what the circuit was designed for reduces the feedback, increasing harmonic distortion (bad) but decreases any transient distortion (maybe good, depending upon the circuits overload immunity). Using a tube with more gain than the design goal increases the feedback, reduces harmonic distortion (good) but increases transient distortion potential (bad)
Excess harmonic distortion is perceived as muddy sound with poor attacks, but in minor amounts may be pleasing. Excess transient distortion is perceived as hard, bright, and edgy sound and that too is unhappy.
Often "tube rolling" is nothing more than finding (by ear) the tube with the "just right" gain for your particular circuit. No magic here, just use a good tube tester to find the tubes with the right gain for your circuit, keeping in mind that there is a lot of sample to sample variation in any batch of tubes.
Frank Van Alstine