In the timescale in question, the key difference between the two types was that the Fleetline was no longer made available for general sale by Leyland. If the Mods will permit a little bit of thread drift, this situation left traditional Fleetline operators who still favoured a Gardner-engined double-deck bus with the choice of the Bristol VR and... er, well, the Bristol VR. By this time however, many a fleet manager, who had their fingers burnt by the Leyland National, were less prepared to tolerate Leyland‘s somewhat peremptory approach to customers, arguably leading to a gap in the market that eventually became wide enough to drive a Dennis Dominator into, closely pursued by the Metrobus. In the fullness of time, I expect some historians will pinpoint this period as starting the countdown clock ticking towards Leyland’s eventual disappearance.
From a basic perspective, you're right - the Atlantean was Leyland engined, the Fleetline Gardner engined. And the VR came with either.
You've actually got to look back to the mid 60s to see how this all came into being. Leyland, Daimler and Bristol were all "independent" companies in their own right - and each had their own customer base.
Bristol supplied the Tilling group of companies - which eventually became part of the NBC.
Leyland had a following among the BET companies though there were some who also took Daimlers e.g. Potteries. - and some municipals.
Daimler were used by many Municipals and Scottish companies. They did have a following among some BET companies, but it tended to be for certain loyalties e.g. Midland Red.
All of these were merged together in the various buy-outs and mergers that created British Leyland in the late 60s - so BL then had 3 double-deck chassis which were in effect competing with each other, the Atlantean, VR and Fleetline. Each had their own following as well.
The NBC, by virtue of many of its companies being ex Tilling, went for the VR - though there were NBC subsidiaries that bought Atlanteans (London Country, Ribble), and Fleetlines (Midland Red, Oxford South Midland).
Many municipals and SBG companies remained loyal to the Fleetline - and others remained loyal to Leyland.
So BL had a problem - and consolidation was inevitable. Of the 3 - the VR was the youngest (announced in 1966), the Fleetline next (1960) and then the Atlantean (1958), however the Atlantean was extensively re-worked in around 1970 with the AN68 version replacing the PDR series. So by the mid 70s - the Fleetline was actually the oldest design. Add in the decision to close Daimler's works in the West Mids and re-locate production to Lancashire, it was pretty obvious the Fleetline's days were numbered.
This, along with the general supply and production issues BL had, meant there was a gap for others - such as Dennis with the Dominator, the Ailsa B55 and Metropolitan / Metrobus to enter the market. But only the Metrobus really made an impact.
BL's plan was always to consolidate further - initially the Titan was thought to be the way forward - again LT speccing a bus with Leyland - but even with a Gardner engine, that wasn't appealing to many operators who thought it was too complicated and too expensive. Ironically it was the Olympian, which was really the successor to the Bristol VR which won out - surviving the Volvo takeover of Leyland Bus and being in production for almost 20 years.