Given your name, the practical answer is that there is no difference assuming they are properly selected and implemented in the circuit. The exception being the EI core and SE outputs, EI cores were the only ones made with airgaps last I was paying attention. Audio is just not as picky as some would like to make it out to be, sure a torroid in the power supply will let us get away with a more compact layout and make it easier to get the noise specs we want but it is not that difficult to do with an EI core. When you get down to it, they are each different in some vague but highly marketable way.

Edit: I am over simplifying things, there are differences but my point is that in audio work the design execution is what matters.