Ah, I see what your saying, but you threw me off when you said ALL other things being equal. We've discussed the increase in noticeable vibration due to zoom effect on these lenses. It's really just a matter of interpretation, but I took the all things equal quite literally. What you'll find is that the 3.97 and the stock lens are sharper than the 4.35, even if you take the influence of vibration out of the equation - making all other things truly equal. One of the first tests I did was to place all 3 GoPro's on a rock solid table facing out through a window, with a view to the horizon. Vibration was removed from the equation.
I can't speak to the 5.4 since I don't have it, but the stock lens and the 3.97mm are sharper than the 4.35, even in footage shot from a completely stable platform. The 3.97 may even be a smidge sharper than the stock lens, but your mileage may vary as the manufacturing tolerances in the production of cheap little lenses like these isn't that tight. The best indicator we have is the megapixel rating, which is higher on the 3.97, but that's just an indicator that doesn't really tell us the quality of the optics.
Along those lines, it important to note that I'm only comparing Peau lenses, which are presumably sourced from the same manufacturer.