Equivalent vs Substitute
There are many 12AX7-type tubes with different type codes such as ECC83, 7025, etc. As explained in Everything You Need to Know About 12AX7 page; these tubes are really the same thing. They all are equivalent to 12AX7 tubes. In all practicality, these are all 12AX7.
There are also tubes that can substitute for 12AX7. These tubes have different conductance (gain) but have the same pinout and can directly substitute for 12AX7. In guitar amps, you can try different substitutions for 12AX7 to get a different tone.
12AT7, 12AU7, 12AY7, and 5751 tubes are related to 12AX7. These tubes were designed for different purposes than 12AX7, but they share the same pinout and filament voltage. In addition, characteristics are similar enough that they can be substituted for 12AX7.
Why They Sound Different
Ok, we're going to geek out a little here.
The main difference between 12AX7 and other tubes is often described as the gain, specifically the amplification factor. 12AX7 has an amplification factor of 100, where 12AT7 has 60, 12AY7 has 40, etc., so the amp's gain changes by something along that line. At least, that's how it's often explained.
While this is partly true, it's a little more complicated than that.
Tubes like 12AX7 are most often used in a common-cathode circuit. The gain of such a circuit is determined not just by the tube's amplification factor (mu), but also by the transconductance (gm) and internal plate resistance (Ra). All three parameters differ quite a bit between the tube types. These parameters come into play and affect both gain and frequency response, resulting in different tone.
This is why tubes such as 5751 (gain factor 70) and 12AT7 (gain factor 60) still provide plenty of gain and crunch even though they are supposedly much lower in gain. And tubes like 12AY7 and 12AU7 will sound much quieter than the amplification factor implies. In addition, the tubes also sound different due to different frequency responses.
Which Type To Try?
In general, if you want to tame an amp that distorts too easily, you will want to try 12AT7 or 5751. These tubes will give you better control if your amp tends to get washed out as you turn up the gain.
If you want more headroom for a clean tone, 12AU7 or 12AY7 will be your best bet. These tubes will provide a clean tone, but you will often need to turn up the amp.
One other thing to note is that these tubes not only change the amp's gain but will also change the tone. This is because parameters like internal plate resistance (Ra) can impact the frequency response. If the tone is more bass-heavy, it tends to distort more and may seem like you have more gain.
So it's best to get more than one type to see what works best for you.
What About Other 12AX7?
Before trying different tube types like 12AT7 or 5751, you may want to try a different 12AX7 tube first. The differences are subtle but definitely noticeable.
For example, if you are using a JJ ECC83S, which can be a bit darker sounding, you may want to try TungSol 12AX7. And if you are using TungSol 12AX7, a long plate 12AX7 such as Mullard 12AX7 will give you a different tone.
Will My Amp be Quieter?
If you are simply looking to make your amp quieter, we found that preamp tube swap won't always work. This is because swapping 12AX7 with another type changes the tone and headroom of the amp. Swapping 12AX7 is more like tuning the amp's tone rather than controlling the overall volume. If you really want a quieter amp while keeping the same tone, it's best to use an attenuator.