I don't think anybody has any good theory, but core materials are audibly different for sure.
To clarify first - there are two main grades of "nickel":
50% nickel will handle about 60% as much power, per pound, but has about half the distortion compared to grain-oriented silicon steel such as M6. It also has enough better permeability to improve small-signal linearity. It's what Mike uses in output transformers when he says "nickel".
80% nickel will handle a small fraction (1/5 to 1/10th) as much power per pound as M6, but has much lower distortion and much higher permeability. This makes it the preferred core for small-signal transformers, and nearly useless for drivers or outputs.
The third option is pinstripes, 50% or 80% nickel interleaved with M6. Compared to M6, and done right (I for one have no idea what "right" is in this case), it should have somewhat better small signal linearity with somewhat more limited large-signal performance, performing in between the two components.
