Whilst Charlie (topoxforddoc) is correct in that the quality of the transformer is crucial to the quality of a SET amp there is MUCH more to it than that. Internally generated noise has no bearing on the matter BTW and is similar whether SE or push pull. PSRR can be much better in the case of a push pull transformer coupled valve amp though.
The very fact that a valve is operated SE puts severe constraints on what can be achieved by an output transformer though... A gapped core is required to deal with the magnetising effect of the standing current without the core saturating. This means a MUCH bigger transformer must be used to achieve sufficient primary inductance. A consequence of this is that the inter-winding capacitances and leakage inductance etc will be far worse than for a smaller push pull transformer of equal or greater power rating. Magnetic hysteresis distortion will also be much higher in a SE transformer...
Those are "just" the problems in the output transformer itself of course...
SE, whether valve, transistor, mosfet, whatever, is also intrinsically asymmetrical.... if we imagine the signal waveform going up and down around a centre zero point then, depending on exact topology, a SE amp is more capable of pulling up than of pushing down (or vice versa). This is why they have intrinsically more distortion and also why it is predominantly second harmonic distortion. With all SET's I've ever had in you don't even need a distortion analyser to know something is badly wrong as the distortion is visibly obvious even on the oscilloscope screen! Put a 1KHz sine wave in and you will see that the top of it is elongated and the bottom is squashed quite visibly by the time you get to around 5W with a 16W SET. It's only by using them with like 105dB horns that they have much chance of being acceptable as they are only giving maybe 0.05W at normal listening levels.
Various tricks can be used, especially with solid state SE amps, to minimise the problems and in the case of solid state SE there is no nasty transformer in the way, hence plenty of negative feedback (NFB) can be applied to correct the distortion. The combination of these tricks and the NFB means SS SE amps can be perfectly good... if rather inefficient even by class A standards (I should have pointed out, in case it wasn't obvious, that all
true SE amps, no matter if valve or SS, are intrinsically class A). A push pull class A amp using the same heatsinks and PSU would though deliver considerably higher power and with lower still distortion. A simple SE SS power amp I designed some time ago in simulation and which I just did a quick "reality check" with shows 0.002% THD at 20W, non too shabby, but remove the NFB and it's more like 10% THD, as expected....
The limitations inherent in SET output transformers mean that even the relatively low amounts of feedback used in push pull valve amps cannot be used in a normal SET amp. A few may have selectable NFB up to around 10-12dB but most just use zero NFB. 20-28dB is more common in push pull valve amps and 60dB or more in SS.
Such is the technical and economic advantage of push pull over SET that SET became obsolete virtually overnight when push pull was invented and for everything other than the cheapest equipment. SE (but usually pentode and about 3W) was still used in table radios and in TV sets up until the end of the common usage of valves but only for the economy of saving on the cost of two output valves. Equipment with pretensions of quality would often boast of "push pull output stage!".... Up until the likes of the Ongaku SET was resigned to history and hadn't been seen since the 30's...
A SE but Pentode amp which I do have a soft spot for is the Pye Mozart power amp
This is a very clever bit of design! It uses one EL34 per channel, SE, and manages 9W, 0.2% THD and even a damping factor of 30! And it's quite small and light! I'll leave it to any interested readers of this to work out how it manages the seemingly impossible
