We've been to VB and HHI many times and love both! The beaches are VERY different. VB is much smaller and quieter, with coarser sand. There is plenty of room for sand "construction," so take/buy some plastic containers of various sizes to aid in building. At 10 and 11, they would love boogie boarding, but suggest you buy one at Wal-Mart--much cheaper than renting. You can leave it for someone else if you don't want to transport it home. Our boys never ventured very far on theirs, but loved riding them onto the beach. Another budget suggestion: bring/buy a couple of umbrella-style chairs. We rented the umbrella and brought chairs, or rented the combo and added our chairs for the boys. We also have a soft-sided thermal picnic bag that was very popular with our group (what is it about water that makes everyone hungry?). At Vero, you are so close to the beach that it is easy to run back to the room for something, or even to rest for an hour or two.
At HHI, since the beach is quite a ways from the main resort, you'd better plan to stay for most of the day. The beach is very wide and hard-packed. The fine sand is great for building. It is much more populated, and the waves are not quite as large. We did love bicycling on the beach, and rented bikes from a business nearby (it's pretty neat to go it--they put in canoes in the back).
Your kids would enjoy either place. Let us know if you want suggestions on other things to do with kids--we've got lots! Have a great vacation!