Historians claim that of the Princess Royal and Coronation class pacifics, it was the former design that had the more efficient and freer steaming boiler. The Coronation however had the more powerful "engine" at the front end.
I don't think that's right. The Princess Royals were one of Stanier's "nearly but not quite" designs (although this is more apparent now than it was when they first appeared and there were no Duchesses to compare them with), and one indication of this was that the draughting arrangements were modified following experience of the first couple of locomotives. Their reputation was one of being a bit shy for steam, although you'd have enough if you managed the fire and boiler properly. The Duchesses would produce steam as fast as the fireman could stuff coal in, or indeed two firemen in special cases; and since the front end was less restrictive they also had a greater capacity for using steam, which would make the absolute improvement in steaming ability required to produce the same relative impression of that ability correspondingly greater.
It was decided that 46202 should be significantly rebuilt as a conventional loco in Crewe Works using the "spare" Coronation "engine" and was outshopped in 1952. So at this point it should be noted that 46202 had the more powerful Coronation "engine" and the better steaming Princess Royal bolier.
The 6202 boiler was different again, with a larger superheater than the standard and also with altered draughting arrangements appropriate for the continuous rather than intermittent blast. I don't know what else was done to it when the engine was rebuilt as a reciprocating machine, but something would have been, since at least some degree of modification would have been a necessity. It might have been altered simply to be the same as the rest of the class's boilers at the time, of course, but there's no a priori guarantee of that.
Unfortunately, A rather special class 8 pacific was being outshopped from Crewe works at that time. so some would have regarded it a little ignominious of British Railways to rebuild "super Stanier" "Princess Anne" which almost certainly would have outperformed "Duke of Gloucester" - cetainly in it's initial period of service. Sadly I am not sure any trials were held to discover just how much of a monster "Princess Anne" was in that short period of 1952.
I doubt any were, since it wasn't intended to be; the point of it was straightforwardly to replace all the funny bits with boggo stuff out of the parts bin, to produce a reasonable approximation to a "standard" (not "Standard") locomotive.
The DoG had nothing to do with it; that only came into existence as a result of Riddles jumping on the opportunity provided by the loss of 46202 necessitating a replacement Pacific to insist on that Pacific being his new design - which needed a fair bit of insisting to overcome the objection that with dieselisation being the favoured policy there was no need for any new steam designs so why bother, but he seems to have been quite good at insisting. Had 46202 not been wrecked there would never have been a 71000.