The 12AX7 is great for noise and low distortion, but is bad at bandwidth, making it a poor choice if you want passive EQ. The 6922/6DJ8 has good bandwidth, but the design of the tube is not for audio: while very good linearity, the design is prone to excessive microphonics. IMO anything designed with them will exhibit a sonic signature that has a lot to do with microphonics.
12AT7s are also designed for audio and have less microphonics. They are also higher mu yet allow for wide bandwidth and so seem to me a good compromise of gain vs bandwidth vs coloration compared to the other two types, assuming that you want passive EQ.
So in this case we see that the design of the circuit says a lot about what the tube choice is, for example if you are running feedback for the phono EQ the 12AX7 can do quite well.
12AT7s are also designed for audio and have less microphonics. They are also higher mu yet allow for wide bandwidth and so seem to me a good compromise of gain vs bandwidth vs coloration compared to the other two types, assuming that you want passive EQ.
So in this case we see that the design of the circuit says a lot about what the tube choice is, for example if you are running feedback for the phono EQ the 12AX7 can do quite well.