Whether it's critical or not will depend on the application, no doubt. I work mostly in audio, where reliability and durability are more important than anything else. The actual dielectric doesn't matter much, but construction quality does. The only exception is where customers are interested in authenticity. This can effect value. Few people think money is unimportant
.
In my edition of Horowitz and Hill
The Art of Electronics there is a table of capacitor dielectric properties, including Accuracy, Temperature stability and Leakage. Rated against these criteria polyester gets Good, Poor, Good. Polycarbonate gets Excellent, Excellent, Good. Polypropylene gets Excellent, Good, Excellent. So at least two people think they're not all the same.
Cheers,
GJ