The biggest issue I can see when switching from PTFE to PEEK is chemical compatibility. PTFE is basically inert, and has far better compatibility than PEEK with most fluids/gases.
When used as a seal material in valves there is a big difference in mechanical properties between PTFE and PEEK. Unfilled PTFE has virtually no mechanical strength and readily cold flows when subjected to any sustained pressure, while unfilled PEEK has fairly good mechanical strength. On the other hand, a PTFE valve seal would produce less friction, less wear, and have better conformability with the mating part than a PEEK seal would.