Regarding a tube integrated amp, do you think the bigger difference in sound comes from the rolling the pre or power section ?
It depends on the design.
A good tube amp will simply amplify with no sound of it's own, just like any good solid state amp (or almost ANY solid state amp). With a good design, tube rolling won't make any difference as long as the tube is correct and in-spec. An "unstable" design will change with normal tube variations or when you swap tubes or as the tubes age
solderdude mentioned transformers. Tube power amps and the power-amp section of an integrated amp requires a transformer to drive the speaker. That's another potential source of sound degradation and good ones are expensive. Because of the output transformer,
it's easier (and less expensive) to make a good tube preamp than a good tube power amp. Of course you can't easily swap transformers.
If a tube amp does have audible distortion or frequency response variations, etc., it's going to sound different from any other amp. There is no one "tube sound".
solderdude also pointed-out that transistors and MOSFETs vary. But just like a GOOD tube design, the performance of the completed amplifier doesn't vary significantly, and will stay in-spec as long as the transistors/MOSFETs are in-spec. The difference is, transistors/MOSFETs don't age and "wear out" like tubes, and of course they are not easy to swap. Op-amps are sometimes in sockets so some people like to swap those, but it usually only makes imagined differences.
P.S.
This is 2025, not 1955, and there is no advantage to this outdated technology.