There are discussions about the different types of film capacitors. They all seem to boil down to the type of dielectric.
The most common polyester (PE) and polypropylene (PP) have similar dielectric constants, but differ by their dissipation factor, better for PP. That's one of the reasons why some designers prefer them. A low dissipation factor is a welcome property in power applications, however there is no definite proof it results in better audio performance.
It certainly has an effect when the capacitor is used in a resonant circuit, but when used as a coupling cap, there is no predictible effect, unless it is undersized.
Dielectric absorption (DA) is another parameter that influences distortion, but is rarely specified.
Most Wima capacitors that are considered good solid performers are PE.
Dedicated "audio" capacitors resort to fancy dressing, like gold foil or Listz wire but the effects on performance are elusive.
In the particular position of plate to transformer coupling, even an electrolytic can deliver perfect performance, whatever preventions some may have.
Polystyrene (PS) is a very high quality dielectric, but only available in relatively small values (<33nF).
Polycarbonate (PC) is also a very good performer, but seems to be unavailable.
Indeed there are various other dielecrics (among them paper) but they are not pertinent to this application.