1.VerbTo be short of accusatory evidence against (a person).
"Relax. The cops have nothing on us. All they can prove is that we were in the same town on the same day."
2.VerbTo lack an advantage over, to not be in a better position than, to be nonsuperior to.
"His Mustang has nothing on her Corvette. [ = both cars are fast, and his cannot beat hers, although perhaps her car is not much faster (ambiguous)]; Even the quickest street-legal cars in town have nothing on a Top Fuel dragster. [ = understated sense: a Top Fuel dragster is considerably quicker]"
3.VerbTo be considerably inferior to.
"Even the quickest street-legal cars in town have nothing on a Top Fuel dragster. [ = understated sense: a Top Fuel dragster is considerably quicker]"