Having visitted both resorts I would say, for quality there is no real difference between them. Both are top class resorts. As far as the "ambience" of each resort, Vero has more the feel of a hotel, HH more laid back and spread out with the buildings surrounded by Oak trees and Spanish Moss.
IMHO the pool on grounds is the main pool (with the feature slide), while the pool at the beach house is a "splosh about" pool so I'd disagree with ncligs on that. At the beach there is only the beach house, a snack bar and the Beach house pool. The beach house is a couple of minutes by car or 15 minutes walk. While it is an inconveniece not having the beach on your door, like Vero, I do think the beach at HH is significantly better than that at Vero. The beach is much wider, much less of a drop off once your in the water and the surf is much calmer.With younger kids HH is a much more restful venue than Vero. while Vero wins on proximity to the beach, HH wins on proximity to bars and restaurants. The marina by the resort (maybe 70 meters away) has several to choose from ( as well as several shops) and there are dozens more restaurants within 5 minutes drive.