Actually, it depends. If the IP4 case is designed for AT&T only, it will be difficult to fit as the mute switch is moved for the VZW 4 and all 4S models.
Look for a case designed for the VZW 4 and 4S, and you'll be fine. Most companies revised their cases anyway to fit them all.
Not all the iPhone 4 cases work for iPhone 4S, It depends on the case's design.
Such as Vapor Pro and Vapor COMP cases work for iPhone 4 and iPhone 4S, But others may do not.
Some do some do not, it depends on how big the cut out is for the mute switch, Apple had to move the mute switch down closer to the volume buttons by half a millimeter or so.