Did some empirical tests on this a couple of decades ago (rather than believe the manufacturers story)...OK I was bored.
DTD 585 (MIL 5606 E) the mineral oil lit in the bunsen burner and we could not put it out...once withdrawn from the heat source.
The Phosphate Ester (Skydrol) fluid is "Fire Resistant" and it depends upon how you do the test....the test methods above are tightly controlled. In liquid form could not get ignition even in the bunsen burner...in fine spray form went like a flame thrower (but again as soon as the ignition source was removed it went out).
Bottom line if you have a TOTAL break of a brake pressure line onto hot brakes mineral oil is likely to ignite and PE won't.
If you have a pin prick failure of a brake high pressure line (as tends to occur on the weakend radius of a pipe bend if hit with a stone chip) then the fine spray is just waiting for an ignition source.
The main advantage of PE fluids is weight saving....over a hundreds pounds on a 747. Over the life of the aircraft very significant.