I would not say brand sensitive at all. I would deem them "circuit sensitive". As far as technology based, polypropylene seems the most cost effective for loudspeaker crossover networks but in high sensitivity designs, some "capacitor compression" that oil and paper gives does sound usually more "musical" although their burst response time lags some. As far as power supply storage caps go, electrolytic have been the mainstay due to economics. The price of polys for PS caps is absorbanantly expensive.I also like the basic paper and wax mallory caps that can be found NOS still.
I reckon the type capacitor to used is based on its audible effects depending on what circuit it is used in and how close to MWV you decide to employ it.
One very common misconception in loudspeaker upgrades is to substitute a different type of capacitor of the same value and call it an "upgrade". Loudspeakers are initially voiced around what is used stock. When folks go and put different kinds of caps in a great loudspeaker system as an "upgrade" the intended voicing is changed. Good or bad, I would not call that usually an "upgrade" unless the loudspeaker was needing improvement in the first place.