I've also stayed at both of them. In my experience, HH is difficult to get during the US main holidays, especially June, July and early August but is easier at other times. The weather in winter is less reliable being further north so in the winter you can pick up studios there for as little as 6 points a night in January (the 'cheapest' in points terms at Vero in January for instance is 14 points per night). Vero has its peak times too of course but they are probably more spread out. For instance, you couldn't get 4 nights over Easter in a studio right now at either resort.
Vero is actually on the beach - no roads to cross etc - but it is a drive to anything else you might like such as restaurants or a bit of shopping. Hilton Head is not on the beach, being about a half a mile away, but Disney does operate a shuttle service to its beach house, where there is also a pool and snacks facilities etc. From HH resort you can actually walk to a couple of restaurants, which is as well since there is not one at the resort.
Both resorts have a programme of activities for children with pool games etc.
Vero is only a couple of hours and about 100 miles from Lake Buena Vista area, whereas HH is more like 350 miles and five and a half hours' drive. If we go to HH, I like to combine it with a few days at either Savannah or Charleston.
I like Vero for relaxation but never go for more than 4 or 5 days. For HH, I am happy with 2 or 3 but agree that both are very nice resorts.