Not from personal experience, but the R/R Spey mod for the UK F-4K amd F-4M aircraft was a mixed affair.
Cost. These were expensive Phantoms, the cost of developing and flight testing the new engine, but also cuts in the numbers ordered.
The RN ordered 59, but got 52. 48 were operational, but 28 were immediately taken by the RAF, due to the rundown in the RN's carriers.
If the CVA-01 big-carrier programme had not been cancelled in 1966, the RN would have got up to 140 aircraft, assuming 3-4 CVA-01's built.
The RAF Ordered 148 F-4M's, but only 118 were built.
In many respects the Spey engine was disappointing, it did not improve performance across the board. Partly this was caused by drag due to airframe mods. to accomodate the larger Speys, especially in the rear fuselage.
J79 Phantoms were faster at higher altitudes, and accelerated better, the complex afterburner in the Spey was slower to light up too.
However, the Spey had some advantages.
Speed, acceleration and fuel consumption were better on Spey F-4's at low altitudes. This was significant, as from 1968-76 most RAF F-4M's were used in the attack role, before the Jaguar released them to provide a much needed boost to UK air defence.
Also, the Spey was smoke-free, unlike the smoky J-79's.
After the Falklands war, the runway at Port Stanley was lengthened to accomodate a RAF F-4M squadron.
As the Cold War was on, UK air defence was already understrength, and the Air Defence Variant Tornado was still a few years from widespread service, 15 ex USN F-4J's were leased to the RAF, for 74 Sqn.
So the RAF ended up with some J-79 Phantoms eventually!