You need to check the cable/housing friction. The derailleur spring must pull the cable through the housing to shift toward the small cogs. If there's too much friction it will be sluggish. You replaced the derailleur, and the shift lever always moves the same amount in each direction, so that leaves the cable. Kinks, problem at the ferrule and cable corrosion or grit in the housing are all possibilities. I suggest lubing the cable with a light oil as it is being put into the housing (never grease).