A 3/4" diameter hose will always have less pressure drop than a 5/8" hose over a given length and flow rate. At a flow rate of 2 gallons per minute the pressure drop would be over 50 feet would be minimal (both less than 1 psi drop) At 10 gallons per minute you'd get about 5 psi pressure drop on the 3/4" hose, and about 15 psi pressure drop with the 5/8" hose. Flowing 20 gallons/minute the pressure drops are about 20 & 50 psi.
So - check your flow rate from the tap. If you have less than 10 gallons a minute, you probably won't see much improvement with flow with the bigger hose.
btw - the length has a linear effect on the pressure drop. Double the length, and the pressure drop doubles (+/- a hair)