I donīt know any airspace where separation standards are connected to RNAV.
But: When working PRNAV flights there is less need to lock aircrafts on headings during "close" crossings etc. In our TMA I can climb one aircraft on a SID that is 6nm from a STAR without having to lock anyone on headings, i.e it is less workload intensive. (separation in such situations 5nm, not 3)
Same situation last year, before we went all PRNAV, you could not trust aircraft to stick to the SID/STAR centerline, and you had to radar vector much more, and by that creating much more workload.