I have played TOC 5 times now, and on one trip, played HT in-between rounds at TOC. I concur with the consensus here, TOC is a superior course. Externalities included, it is a landslide - the beach, scenery, family atmosphere, food, etc. are top notch at Kiawah. But from a strictly golf perspective, I enjoyed the variety and difficulty of TOC much more than HT. The par threes at HT are really terrific, but overall the course leaves me with the impression that it is simply tight. That is of course by design, and tree growth is constantly growing stricture for most golfers. TOC by contrast seems vast at times, and the winds and vistas help to accentuate this feeling. I took a caddie at HT, and really regretted the experience as I was paired up with three players who rode in carts - in contrast to the the walking only experience at TOC.
TOC is really two distinct nine hole tracks, and each plays dramatically different with the shifting winds. Each nine has several crescendos and diminuendos and there are a variety of reasons that the course challenges the player. Conversely HT has at times a monotonous feel, and it is hard to remember an adjective other than "tight" to describe the course after the immediate memory fades.
I have to say though, what a great trip! I'm very jealous, and essentially, you're asking us to help you choose between molten chocolate cake and chocolate soufflé.