Let's say there are two diets, consisting of entirely different proteins. If you split up all of the proteins from one day of each diet, you'll get the same set of amino acids and the same count of each. Assume everything else about the diets is the same.
Would these diets have the same effect on the protein composition in your body? Different polypeptides, but overall the monomers are identical. Does your body break down proteins entirely, or will it reuse some chains of amino acids?