Push-pull amplifiers make more power, but often do so with increased 5th harmonic distortion, which causes them to sound brighter. This is not always the case though, if the amplifier is fully balanced from input to output the only distortion component will be the 3rd harmonic, which is considered one of the lower ordered harmonics and is more innocuous.
A pentode amp will make the most power for the tubes involved, but will also be the least linear, and so will need negative feedback to linearize it. There is a price paid here- you get most forms of distortion reduced, but with an increase in the odd ordered harmonics, which the ear finds unpleasant.
Ultra-Linear is a method of using the output transformer as a very local feedback loop to linearize the output section. The result is an output section that that has nearly triode linearity, and nearly pentode efficiency. This is a very nice way to set up a push-pull amplifier, but if the amp were actually using *real* triodes, it would sound even better as it would be more linear.
Output transformers are such that the bigger you make them, the harder it is to get bandwidth. This is particularly true of SETs, and is a primary (no pun intended) limitation in the higher-powered examples. In most cases, the 7W of a 300b is about as big as you can get and expect bandwidth that might be considered 'hifi'. This is also why the smaller SETs, the 2A3s, 45s and the like have the reputation for sounding better- they have greater bandwidth. Now you can fudge things a little- optimize for bass or highs (and since most high efficiency speakers have troubles making deep bass, the tendency is to go for the highs rather than the bass) since you aren't going to get both.
Push-pull overcame a lot of these issues to a certain degree, with its own set of trade-offs. For example, an SET will have nearly unmeasurable distortion as the signal level heads towards zero, whereas a push-pull amplifier will usually see increased distortion (this is commonly attributed to an additional circuit in P-P amps called a phase splitter; its worthy of note that not *all* P-P amps have to have this as a separate circuit). This is where SETs get the magical midrange that they are known for- when distortion is reduced, detail is revealed.
You still have the issue of bandwidth with P-P, but in general you can have about 10X more power available compared to an SET with equivalent bandwidth.
The DC that the power tube draws through the transformer of an SET can cause saturation (distortion) issues with the transformer. This is a major design consideration of the OPT for an SET. You don't have the DC saturation issue with P-P, as the DC currents used by the power tubes cancel in the core of the transformer. On top of that, even-ordered harmonics are also canceled in the load, making for an amp that should be more transparent at greater power outputs.
The distortion of an SET is mostly lower orders until the output power becomes significant. At that point the higher orders become significant (although measurably insignificant) to the human ear. The 5th, 7th and 9th harmonics are used by the human ear to determine sound pressure, so when they are distorted (even so slightly that it is difficult to measure) the effect is that of increased loudness. Since more power is usually used on transients, what you have is the loudness cues occurring on the transients. The result is that SETs will *seem* to be very dynamic for the amount of power that they have, and often people will say its all the power that they need- they don't want to turn it up any higher.
So now you can see that in conversations about such, that if you substitute the word 'distortion' for that of 'dynamics', the meaning of the conversation will not be altered! It happens that if you can eliminate the odd ordered distortions, the amplifier will have no loudness cues, and the immediate effect will be that of turn the volume up higher, as it does not sound 'loud'.
Now IMO and IME, 'loud' is something that a stereo best not do, **regardless of the actual volume**. That can be a bit of a trick, but is well worthwhile.