There are many differences, but the ones that make the biggest difference are the Gain Factor and the Plate Characteristics (including the Grid Voltage Curves).
The Gain Factors for each are as follows...
12AX7 = 100
12AT7 = 60
12AY7 = 40
12AU7 = 17
Keep in mind that this doesn't mean you can put a 12AY7 (40) into a 12AX7 (100) socket just because it has a lower gain. First thing to consider is that the bias circuits for a given socket are designed such that the spec'd tube will operate in the center of the load line - which is based on a given socket's supply voltage and the Plate Load Resistor. If a tube other than spec'd is used, then either the top half of the signal will top out early or the bottom half of the signal will bottom out early. Ya want them to "clip" at the same time to max the level of that stage. The second reason is gain structure. If one stage drives the next with too low of a signal, then some of the dynamic range is being thrown away. In other words, you'll have to turn up the amp to get the same volume and you'll be turning up the noise floor with it.
In summary, stick with the spec'd tubes for a given amp, or have a qualified designer (not a tech) mod it to use a different tube - even then it's a slippery slope. IMO, the older stuff (Fender, Marshall, etc) stuff is so well designed you'd be hard pressed to find a tube tech, or weekend warrior designer that can actually improve it.
I hope this helps.
lovechild
www.lovechildamps.com