Two different pumps/designs.
Your old one.....4900.....was a variable speed pump that used a microprocessor to control output based on demand.
Your new one.....4048...is a constant speed pump that uses a spring loaded bypass to control output demand. That is why you getting some pulsing. Speed is constant but flow can fluctuate due to bypass diaphragm cycling. (Bypass allows flow from discharge to go back to suction side)
4048 is a good pump. Enjoy it.
And don't go messing with bypass setting and/or pump discharge setting unless you have gauges and fully understand how the two work with each other....otherwise the pump will not turn off if you mess the settings up.