I like Nylatron the best, followed by phosphor bronze, with soft synthetics like Teflon washers way at the back of the list. Nylatron is an excellent compromise between the rigidity of a metal washer and the lubricity of a Teflon washer. In my opinion, the advantages of phosphor bronze as a washer material are vastly overstated. For example, claims of better reliability in hot environments. Nylatron can be used without compromise in ambient temperatures of up to 220 degrees Fahrenheit. It's certainly true, however, that phosphor bronze is capable of resisting more than that. They are also most definitely stiffer. They also exhibit significantly more friction against steel than any of the synthetics used, including Nylatron. They are more resistant to chemicals - strong acids and bases in particular - but when was the last time you went cutting something with your knife completely immersed in an HCL dilution or similar?
For me, Nylatron provides the best opening "feel," as well as being effectively maintenance free - i only have to worry about keeping the washer area free from dust and moisture. I never lubricate my knives with Nylatron washers. Use your own judgment for this question - there are material data sheets for Nylatron and phosphor bronze all over the Web. Don't let materials properties charts dupe you into declaring one material "superior" to the other, though - use them first, then decide based on how you like them. The only thing that washers in folding knives have to do is resist compressive forces and allow a smooth, unimpeded opening action for the blade. Even soft Teflon can do that for generations if it's thick enough. Bending forces - any force applied strong enough to bend the washers will also, almost certainly, warp the liners or crack the blade in half. Consider this as well - in the freak case where your washers do flex significantly, synthetics will pop right back into place, while phosphor bronze will take a set. The possibility of exerting any significant mechanical force against your washers (with the exception of compressive forces generated by the pivot screw) without exerting damaging forces on other components of your knife is almost nil.