It is a rare person that can taste any difference between hard and softened water... and "feel" is not a very reliable test. You can buy a hard water test kit at most hardware stores or big box stores and you should test both the hot and cold water and they should give the same result but many times the hot will be hard due to softened water dissolving hard water scale in the water heater, adding hardness to the water until all the scale is dissolved.
Does the control valve meter water use; with water running in a tub wide open, does it count down gallons or indicate the water use?
Have you allowed it to run low or out of salt?
Do you have a toilet flapper valve leak or is the water level in the tank too high and overflowing into the overflow tube? Any other water leak; garden hose, outside tap, under any slab construction? If you are on 'city' water, make sure no one uses water and go watch your water meter for 15 minutes to see if it counts any water use. If on your own well, does your pump run at times when no one is using water or, watch the pressure gauge for 15 minutes to see if the pressure falls.