I would definitely use horizontal walls if using foundationless frames. The main draw for me in using §¤«£¿æ's design for the tbh, with angles sides, was the claim that bees tend to connect the comb to the angled sides less. In my tbh, which has angles sides, I have had very little trouble with comb attached to the sidewalls.
With frames, this is a non-issue. Charlie's hive design gives you the best of both worlds. The bees are building horizontally. You don't have to lift heavy boxes. You can expose one piece of comb at a time. These are tbh benefits. But using the frames, he also has the lang-type benefits of interchagability of equipment with other beek and his own lang hives. The comb is a bit sturdier and easier to extract, if he chooses to do so.
The original poster is getting into beekeeping here in the U.S. Charlie's design would allow that newbee to have the best of both worlds. Foundationless frames in a long-box. If he begins with a couple of hives, there is a good chance one or the other will struggle. If his "more natural" hive is struggling, another more experienced beek could give him a couple of frames of brood to slip right into his hive. If he's the only beek around with his size box, that gets much more difficult. (Speaking from experience)