It's absolutely the lower profile, that's why plant saucers are often recommended for hatchlings as an ideal hide, along with things like tortilla holders, low-profile tupperware, etc. They don't like having an open ceiling above them, even if it's solid -- they're prey animals that are readily picked up by pretty much everything that eats them. Up is bad.
And one of the main reasons for identical hides being recommended frequently is this exact question being posed -- the hides being identical means that an animal sacrificing thermoregulation for security/preference won't be something you have to consider when the animal is exhibiting behavior like this.
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