You won't hear so much difference between Tetrode and Pentode, but you will hear a difference between Ultralinear and the others. Ultralinear allows the tubes to approach triode linearity, while retaining most of the power that Tetrodes (or Pentodes) otherwise make.
So Ultralinear circuits make less distortion and tend to have a lower output impedance. If the designer is crafty and takes advantage of this, the result will be an amplifier that is smoother and more detailed, as removal of distortion usually has that effect. Ultralinear amps need less loop feedback in order to work, and in some cases don't need any at all. Loop feedback adds brightness to almost any amplifier, so if you can run without it you can have a more relaxed presentation.
However, not all designers will do that, so YMMV.
So Ultralinear circuits make less distortion and tend to have a lower output impedance. If the designer is crafty and takes advantage of this, the result will be an amplifier that is smoother and more detailed, as removal of distortion usually has that effect. Ultralinear amps need less loop feedback in order to work, and in some cases don't need any at all. Loop feedback adds brightness to almost any amplifier, so if you can run without it you can have a more relaxed presentation.
However, not all designers will do that, so YMMV.