If you're not into sport riding then the H rated Dunlop should work fine for you. Some people noted it was more prone to slip during cornering which is to be expected for a harder rubber.
H rated tires are standard on most touring and standard cruisers including the new Rocket Touring and I think the Rocket Classic as well. I wouldn't worry about it if you're not aggressive in the corners and usually stay below the 130 MPH rating.