Just did my LPC and of course came across the PRNAV approaches.
The big advantage is, that there is no need of any ground based equipment. Maybe in a place like LHR or any other big airport in an established and well run aviation environment, there is no need for this advantage immediatly, but for a lot of other places especially on the black continent, this is a major advantage.
No need for special ground based equipment, except of some lightning and a maintained runway, meens no problems regarding maintainance and of course serviceability of ground based navigation aids. How often do you find that the navaids are not working propperly or are unservicable.
One further advantage is that the PRNAV approaches is that they are usually straight in approaches and don't have an offset, like a lot of VOR based approaches have, if the VOR station is not ligned up with the runway centerline. This helps a lot, I am sure.
At the end I think in a lot of places like LHR or JFK we will see in the future that PRNAV approaches will become the backup approaches to the ILS, while NDB and VOR based approaches will become more and more unpopular, as the ground based navaids can be decomissioned, which aids also in costreduction. For places in less developed parts of our planet the PRNAV approaches will become very popular for the above mentioned reasons.
I must say I like this kind of approaches very much and think the procedures are well defined. Just my aircraft type can be a bit tricky in respect to the VNAV part, especially the speed. But this is just a matter of design and/or training.