The question is Was the 5in DP gun better for AA defence compared to the twin 4.7in RN destroyers gun. There is no doubt that all the RN officers who observed both in action believe that the result is yes, the 5in was a much better weapon. No one has even tried to quote an RN officer who believed that the twin 4.7 was even close to being as good as the 5in. We have opinions, theories but no quote from anyone at the time.
To base the defence against this on observations that the USN believed that the 5in wasn't as good as they liked is a different answer to a different question. I am very confident that the RN would have been absolutely delighted if their Heavy AA guns had shot down 18 percent of the suicide aircraft. To claim 39% of all kills in the period Jan - July is a remarkable achievement.
There's a huge difference between claims and actual kills. My look at USN AA kills as stated by Lundstrom leads me to believe that the actual 5in kill rate during 1942 was around 5 to 10%, at most, of total AA kills. After 1943 the USN began using VT ammo in large quantities, so one would expect an increase in 5in AA efficiency, but it seems to me that the decline from 1944 to 1945 was mainly due to increased accuracy of reporting and that the 39% claim for 1944 was greatly overstated.
However, if 5in AA was ineffective (and it was) in 1942 and if RN 4.7in AA was similary ineffective, then there would be a greater reliance on the CIWS, and thus the RN policy of of saving weight via lower elevation main armament but ensuring a heavy CIWS was justified, and that total RN AA efficiency and kill rates would actually decline if RN destroyers were equipped with MK37+5in/38 at the expense of their CIWS. This trade off is not something that anyone in the RN could have known, given how greatly inflated and misleading USN AA stats were during WW2 - especially given that RN AA kills seems to have been much more conservatively stated.