Myrtle Beach and HHI are two separate beach worlds and hard to compare the two.

We love both and it all depends on what they are looking for.
HHI is a great relaxing, family resort area. There IS a lot to do but it depends on what your boys like to do. There are a lot of eco-tours, fishing, crabbing in the area and day trips for history are at your finger tips with Charleston, Beaufort and Savannah. My kids love history and taking some of these day trips break up the beach days. Boys your age would love the history of Charleston. You also have South Beach in Sea Pines with the Salty Dog, lighthouse, etc. Golf is the big draw in HHI with some nice mini-golf places as well. A PP talked about the vacation villas of Marriott. There is another one called Marriott's Surf Watch which is the best place in HHI we've ever stayed.
Disney's HHI is also great, the drawback for me is that the beach is across the street.
Myrtle Beach is fun beach, think more commercial, not as relaxing, always on the go. Tons of mini-golf, more touristy stuff, the best mini-golf anywhere on the planet! Great shows, shopping, chains like Hard Rock, Ripley's and water parks, rides on the boardwalk.
Think like Disney on the beach. The Grand Dunes Marriott is really nice (can you tell we're Marriott people?) and someone just posted a new place with a great indoor water area but I can't find the thread at the moment. Maybe someone knows what it is. I think it has Villages in the title. Think highrise, busy beach though when thinking of MB.
Both are great and both can be done within a reasonable budget depending on what you want.
Overall though, relaxing, more upscale=HHI
fun, on the go=MB
Have fun! Would love to know what your family picks.