Shower heads have flow restrictors so pump reaches full discharge pressure and then pressure switch turns pump off.......pressure drops so pressure switch turns pump back on.
This pulsing causes differences in hot/cold water flows.
You could remove restrictors (some are in end of hose where it connects to faucet, some are in end of handle, some have to be drilled larger vs removal)
You could change out shower to an Oxygenics Handheld Shower......may smooth out flow demands.
You could install an accumulator tank on pump discharge which can decrease pump cycling
You could mess with pressure set point....adjustment screw on end of pump head.
BUT depends on type of pump.
