The Rangers are a much bigger club and have more history but the Islanders have had a very succesfull perio in the 80's and are usually seen from people outside of New York as the cooler team to go for.(Kind of like West Coast and Freo, with the ranger being wce and islanders being freo). Also alot of people in NY go for the New Jersey Devils because of thier close distance.
In all honesty if you're gonna go for a NY team I'd say Rangers. they're currently a better team and actually play and represnt NYC, where as the Islanders represent more of Long Island than the actual city.