Just sort of ruminating on this (and it's probably obvious & old news to many here) but I think that the UK MOD obviously came to prefer the Rolex Oyster case/crown structure but mandated that Rolex duplicate Omega Seamaster 300 hands when granting them their contract:
We know that in fact the SM 300 was issued by the MOD several years prior to the Submariner.
We know that the "Niad" pressure-fit crown system on the Omega was highly unreliable and prone to flooding in shallow water.
This then necessitated retrofitting of a screwdown crown (denoted by the "A" prefix) on the SM300 and this most likely also disenchanted the MOD regarding the Omega's suitability for the required duty.
I have heard that there is not really much to chose between the Seamaster's cal. 552 and the Rolex 1520. Of course, watchmakers love those pre-1970 Omega movements because they are easy to service!
Nonetheless, I do not believe movement was the reason for the MOD's decision to switch.
I am not sure about the price component but can't imagine that the SM300 was much more expensive than a 5513, if at all.
And so we have to conclude that the MOD turned to Rolex because of their superior water resistance...with the proviso that they adopt the more legible Omega-style "Gladiator" hands and spear-tip sweep seconds (and maybe even the 60-tick bezel). Hence:
(Photo from VRF Archive by Mike Wood)
Like I said, I don't think I'm breaking any new ground but just wanted to write it out for my own--and other MilSub novices'--benefit.