Toroidal vs EI power amps any difference.

Good question but you've ignored tube amps were EI reigns dominant.  Toroids are cheaper and lighter.  There are some differences in capacitance and resistance.

OK. that's the limit of my knowledge so now I'll speculate a little.  Transformers are more important in tube amps. (not sure everyone will agree with that).  Transformers for tube amps are more expensive (still, the question is cause or efect, could tube amps be made better with toroids).  

I'm leaning toward the conclusion that EI transformers provide higher quality outputs but SS amps can get by with toroids with filtering.  I will add that toroids are newer and when they were introduced there was a lot of bragging and marketing.  SS amps still often brag about them in their literature, whether is is appropriate or not.

Lastly I am having a custom hgh end amp made.  The transformers are being hand wound in Bulgaria.  They are EI transformers.

I'm eager to see what others have to say on this topic.

Jerry

Toroidal transformers are more compact and efficient. They generate less EMI, so are less likely to interfere with other circuits. If well potted, they can also be better mechanically isolated (less chance of buzzing). The biggest downside is they do a much worse job filtering any noise on the incoming AC, so more external circuity is required to do this. 

The components in my system that sound the best use R-Core transformers.  These use a continuous conductor and have opposing windings to cancel out magnetic flux and have ultra low noise.