Haven't been to JW, so this is comparison of just LP and HC.
Been to LP many, many times and went to HC for the first time over the 4th. Both are excellent and have subtle differences. LP is more sprawling and has certain activities that HC doesn't have, like kayaking and horseback riding. HC is older and more compact, so you are always a lot closer to activities for the kids and pools. Also much easier to get a drink at the pool bars, and they also had little bars set up outside on walking paths every night, and a "float up" bar on the lazy river. The trees and natural beauty at HC seemed more mature. Lots more shade.
After being to both, I lean slightly toward HC being better. The proximity to "the action" was better. It had a better water slide for the kids (not JW, but better than LP), and the lazy river, "beach" and pools were better and had more natural shade.
Another big plus for us was the proximity to Sea World and other things in general. At LP, you are pretty secluded and resort-bound. It takes 10 minutes just to get back to the highway near Bastrop. At HC, it is no big deal to get off the property and you can be at Se World in 5 minutes and at the River Walk in probably 15.