One thing you have to t
I've read that there's a certain coloration/tonality that the 12ax7 design brings to the table. From a thread on the gear page (in the context of guitar amps, of course):
The 12ay7 is like playin' your guitar,only louder.
The 12ax7 is like playin' through an amp (colored).
The above is kind of simplistic, but I tend to agree
Things you all have to take into account is the circuit for each tube.. 12AX7 -Highest gain audio tube, Plate resistor typ 220K, very low current approx 1ma, reduced hf response. 12AY7 - Medium gain audio tube, Plate resistor 20K to 50k, wider bandwidth, higher current approx 4 ma.
Assuming you are not just replacing and AX with an AY, and each with their proper circuit values, the AY has rolloff much higher f, and thus phase shift inside the audio band is reduced. And they are not typically used that often as far as I know. The AU7, for instance, is used where you need some power, like driving a reverb spring or as a low impedance phase splitter to drive the output tubes.
The thing that makes these kind of discussions difficult is the tube is only 1 element of the circuit. With a 50 to 100 other parts in the circuit there really isn't an absolutely better tube for every application.
Each is made for a specific purpose. If you look at the spec sheets the AY is a low microphonic design. Not only is it built to vibrate less internally, its lower gain will amplify its self noise, including microphonics, less. Maybe that leads to a sense of transparency.
Like in golf, a 9 iron is no "better" than 5 iron or a driver. Each is designed to be optimum for their intended use. You may be better at swinging a 9 iron than a driver and feel more comfortable but that's operator error. There's an analogy in there, I'm sure of it.
I don't play guitar professionally so I don't get caught up in the AX controversy. As a hifi tube it's usually used as a phono pre.