Sorry, but there is a relatively large difference in detail between the two. That has nothing to do with dynamic range, simply the pixel size. The D800 resolves quite a lot more detail than the 5D III. That either translates into the ability to enlarge more with the same level of detail as smaller enlargements with the 5D III, or it translates into naturally crisper, sharper images when downsampling for smaller prints or online publication.
Maybe with the very best of Nikon's lenses. But for even their very good lenses, there really is not much of a difference. Which may explain the observations made by the photo club.
There are many comparisons, but, a quick one, the new Nikkor 58 mm f/1.4 on the D800 vs the old Canon 50 f/1.4 on the 5DIII result in 18 p-Mpix and 17 p-Mpix, respectively (using DXO data). I doubt anyone would be able to discern a difference between those two systems.
But yes, put the very best of lenses on the D8xx and you have more resolving power.