Hi Mac ,
It is very hard to point to one thing and the Electrocompaniet amps are a large part of it but not the only reason.
They have total control of any speaker connected to them and the circuit design is unusual and as far as I know unique to Electrocompaniet and Abrahamsen audio , they pay special attention to eliminating timing induced distortions and preserving transients in the music and are the best amps I have ever heard at reproducing complicated and dynamic music , nothing ever seems to catch them out no matter how dense the music gets .
I have loved PMC speakers from the first moment I heard them they have similar qualities to Electro amplifiers but it is only since I bought my PMC PB1i's that I can say my system can do an impression of live music and I think it is mainly to do with deep bass that they produce , my old OB1's could not do it even though they are very good speakers .
So it is a combination of things , put Electrocompaniet and the larger PMC'S together in a good room with a top class source
and good live recording and the magic happens .
With good studio recordings you are right the separation can be better and a image more 3d but the sound has been created by a studio engineer so it is more polished than live music, but I love the rawness and energy of live music .
If I had to pick the thing that is essential for a HiFi system to produce live sounding music it would be very deep, powerful ,
Textured and controlled bass .