Paul, I'm well aware of the spec differences between the AU, AT and AX. I'm wondering what problems might be encountered, though, if I were to substitute a 12AT7 in place of a 12AX7 in an existing preamp circuit.
Atom
It really does depend on the particular circuit. I can offer some generalizations or examples though.
Suppose the 12AX7 is a conventional cathode biased, resistor loaded circuit. It will probably be running the 12AX7 at around 1mA - let's say 300v power supply, 100K plate resistor, 200v on the plate, and 1.6K cathode resistor. The AT7 would run at a similar point; I get about 150v on the plate and 1.5mA. The output current capability is improved 50% but the output voltage swing has become asymmetrical with one-sided clipping happening earlier. If it's a preamp, the reduced peak voltage is probably no problem and the performance is similar to the AX7.
But if you look at the plate curves, you will see that this is at the very bottom, in the region where the AT7 distortion is pretty bad. And the plate impedance is much lower, so if it's in an RIAA circuit the equalization will be thrown off.
If instead you ran the AT7 at the higher current it likes - perhaps 7mA at the same 200v on the plate - then it would have 600% more current capability and the same voltage capability as the AX7 did - a much more robust performance, in a way that may or may not be important in the particular application. It would of course need a more capable power supply.
Hope that gives some of the flavor of the various effects.