(1/0.75)^2 = a factor of 1.8 larger in pipe capacity.
Try these guys for some numbers
The friction loss depends on the water velocity squared, and velocity depends on GPM and pipe size.
IMO the public water supply acts more like a 'pressure source' [constant pressure regardless of flow rate over a zero to 13 GPM range]
rather than acting like a 'flow source' [pressure adjusts to provide a constant flow].
Like Mr. 1971 said, what is your shower GPM, with and without other fixtures running? All you need to check this is a known capacity container and a watch. I'm sure it's less than 6 GPM in any case.