12ax7 vs 5751

What is the difference between 12at7 and 12ax7 ?

I asked Brent Jessee that question but added the 12au7 also. He said the 12ax7 has the highest gain followed by the 12at7 then the 12au7.

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Does that mean they are interchangable? If so I wonder which is preferred...less gain/more volume OR more gain/less volume.
It was suggested to me that the 12at7 Golden Dragon tubes may be my weak link.

Mcpherson -

If you're only considering gain factor, the 12AX7 family falls like this:
12AX7 - 100
5751 - 70
12AT7 - 60
12AY7 - 45
12AV7 - 41
12AU7 - 19

Many circuits can function with any of these, but straying too far from the original gain isn't usually good for the sound. A general rule of thumb would be to substitute as follows:

12AX7 - 5751 / AT7 / AY7
5751 - AX7 / AT7 / AY7
12AT7 - 5751 / AY7
12AY7 - 5751 / AY7 / AV7
12AV7 - AY7 / AU7
12AU7 - AV7

You should always check with your manufacturer. The 5751 and 12AX7 are identical in their limits within a circuit (voltage/amperage) but that's not the case with the others. In most applications you're safe, but you may find it easiest to stick to the 5751 and 12AY7 if you want to try out some different tubes within the family.

+1 Check with the manufacturer first. I have a 5751 in place of my 12ax7 and the manufacturer of my Octave states the 12au7 can be used in place of the 12at7's. So what I have gathered is a lower gain should work in place of a higher gain tube. But I don't think I would want to put in a higher gain tube than what came with it. For the volume differences is so minor it doesn't matter to me. I like the tube that sounds the best.

Now I'll admit I seem to be the oddball here because I've started swapping output tubes before the drivers or input when I got my amp. To me so far the input tube makes the biggest difference in sound.

Xti - The input making a bigger difference than the drivers is a common conclusion. It definitely works that way in my headphone amp.