the 1/1A in sheffield is jointly operated by Stagecoach yorkshire and First South yorkshire and has Streetlights (bith first and stagecoach) and streetdecks (Fiirst)
Generally in Sheffield, Stagecoach are pretty reliable (the 1/7/25/83 are single and the X17/43/50/52/88/120 are double) - the only ones that change are the 44/72 (which interwork) and the 57 (it may just be peak boards that are E400s as the daytime service interworks with the 201).
However First are pretty haphazard with their allocations - pretty much any "frequent" double decker service (say at least four buses per hour) can be single decker (1a/51/52/56/75/76/95/97/98) plus there are double deckers working on the 20/24/83. The only really reliable double decker routes (of any frequency) are the X1 and the 81/82.
There are some predominantly single decker routes though (the 3/3a being the most frequent).
I'm not sure whether this is clever allocation of the biggest vehicles to certain boards or a protest to Head Office that there are insufficient vehicles or just lazy allocations (there are plenty of interworkings on Rotherham area services but less so in Sheffield, so I don't think that interworkings can be wholly to blame).
Makes it interesting, I guess, just a bit awkward for passengers who can't rely on the type of bus they'll get home will be the type they got to work (e.g. modern Streetlite with WiFi but few seats versus twelve year old double decker with more seats but not the same creature comforts on board).