I am not sure what is best. I have had good results with ArmorAll . I will add a word of caution here about really old grips. Pictured is a pair of grips that was on a 39 girl's Schwinn. These grips were hard as a rock and were very difficult to remove. [I don't want to get into a discussion here about removing grips, we have beat that to death]
I decided to soak the grips in water, just about hot enough to boil for a few minutes prior to taking them off. I figured they would soften a bit.Make them a little more elastic and easier to get off.
So with the grips still on the handlebars I stuck one end in a pot of hot water and let it soak for a while.
Look what it did to the color of the left grip. It was just plain water, but really hot.
Now I have since rubbed this grip down with rubbing compound and you can see the color deep down is still there. Not sure if it's worth the effort to spend trying to bring it back.
Also I had at least 6 pairs of old white Chubby 1950's Schwinn grips that I placed in old glass dill pickle jars filled with a bleach solution[ I just love dill pickles ,don't you?]
They never did whiten up. I then let them soak a couple months just to see what would happen. They were ok but not as clean as I thought they would be.
So be careful with old grips. just saying......