Sharpen up to a point, but if a blade is too nicked up or has bee sharpened too much it starts to make more sense to replace.
I use to use a bench grinder, but find that on the whole I seem to get better results with an angle grinder and flap wheel. It takes about the same amount of time either way, but the angle grinder keeps the motor out of the way so I'm not constantly maneuvering around it like with a bench grinder.
This season I've mostly been mowing with a 50 year old Lawn Boy that I'm pretty sure had its original blade on it. I know it's an older style blade as they redesigned the 21" blade in the 80s to not require a separate stiffener which this one has. I threw a new high lift blade on it(all the 2 stroke 21" staggered deck Lawn Boy blades are interchangeable from the 50s to when they stopped making them in the early 2000s) and was amazed at how much of a difference it made in cut quality and, in side discharge, let the mower throw the clippings 6+ feet just like my newer ones do.