Ian,
Vexed question, a diversity of opinions, and quite a bit of controversy.
First, two tcategories of transformers for audio - type I for power suppies, and type II, for handling signals in the audio chain. Type II is very special, and can be outrageously expensive, particularly the single ended output transformer which is quite difficult to wind optimally because it passes a large DC current at all times, typically 60-120mA.
For power supplies, if the rectification and the caps and the topology is good, then the transformer assumes less importance. In fact, you can launch and argument that a transformer with restricted output surge due to saturation, undersize, or plain bad quality, might even sound better. I have agonised over the choice of appropriate power trans for the AKSA/LF/Soraya, finally settling on the toroidal, because it is compact, has low magnetic field radiation at low output, is relatively cheap, and has low profile, making it ideal for the wide, slim cases of audio amplifiers.
There are C cores, R cores, and EI transformers, and others too. All have their advantages and disadvantages. Generally, the choice comes down to cost, size and weight, with performance, measured by regulation under full load (the voltage under full load is expressed as a percentage of the voltage at no load, lower the better).
I have found that the transformer does not make much difference to the sound, although one transformer flaw stands out - mechanical hum. This comes back to how well the core, made of a wound strip for a toroid and laminated plates for the EI, is potted. If not completely covered in potting compound, they can hum as the magnetic field builds and collapses under the mains influence. Hum can be a real problem in transformers if it's mechanical in origin, and toroids can be very susceptible to such problems.
Hope this is helpful,
Hugh
