Some years ago I looked into this in great detail. The findings aren't relevant now but what I found was that the film thickness varied as you might expect but the manufacturer compensated by using backing paper of a different thickness so the combined thickness of film and paper was fairly consistent across brands. The international standard for 120 (and 620) film is not a tight as most people might expect and I did have to check cameras with film brands that represented the extremes of variation at the time.
The one bit of advice I would always give was to try to always use the same brand take up spool as the film being used. If the backing paper edge gets gets stressed due to the spool being too narrow or the film not running on to it in perfect alignment this can have a big effect of the force needed to transport the film.