As has already been stated an 'either or' question is far too simplistic, both rings and radials have their uses.
I think it is worth summarising what I see as some disadvantages of both circuits.
Existing rings...(on EICR's for example) are an absolute pain to verify. Unknown layouts and non-textbook readings mean verifying the possible presence of spurs from spurs, interconnections etc is time consuming and involves much dismantling. Most of us use plug in testing adaptors which often produce odd readings due to contact or switch resistance on ancient outlets, the only certain way is to drop the points and use probes straight onto terminations, disruptive, time consuming and damaging to surface finish. Real time constraints when carrying out EICR's at acceptable cost mean ring circuits are often not properly verified and the inspector has to make judgement calls on whether the circuit is correctly wired. That said I love testing my own rings and calculating whether measured readings are spot on!
As far as radials go there was a long thread on here a while back where an OP stated rings should be outlawed because they are often abused by Kev the kitchen fitter and DIY Dave, his point was radials are much safer.
But unskilled persons being unable to correctly alter a ring is not a reason for banning it, ban Kev and Dave...not the ring!!
That point of view also ignores the potential danger of a radial. One bad or broken connection of the cpc may result in every downstream point working and apparently ok but not having an earth.
I think the safest circuit of all is a radial serving one point from a 16 or 20a OCPD, but the practicalities of that with the number of points modern properties require make it a non starter, not only for the capacity of DB required, but for the sheer quantity of wiring involved.
It is though an interesting phenomenon that many people are completely incapable of altering a ring, and finishing up still with a ring, and not just Kev and Dave. A ring is one of the simplest of all circuits, just a loop of cable which starts and finishes at the same point, and yet it continually seems to generate utter incompetence.