The 5751 tube is indeed lower gain.
Lots of people like higher harmonic distortion. In the absence of understanding what they are listening to, they assign lots of different virtures to distortion pretty much randomly.
To "muddy" the waters further, all things being equal, when you reduce the feedback by using a lower gain active device, you will actually reduce the transient intermodulation distortion, which is excess feedback related. This will reduce any preceived "edge" or "grain" in the sound.
Thus the best sounding tube for you with most equipment will be the one that produces a nul in both harmonic distortion (gain too low - muddy) and TIM (gain too high - bright). Unless of course you really like one or the other distortion aspects a whole bunch (some do).
In AVA tube equipment we design so that TIM cannot occur at all, thus all other things being equal, the best tube will be the highest gain tube possible, that is unless you really like harmonic distortion.
Now of course all you need is a high quality tube tester to find those high gain tubes, unless you are satisfied with the testing and selection we have already done for you in our new products.
Frank Van Alstine