Does the arrangement of amino acids in a protein matter for nutrition?
Arrangement of amino acids determines the protein structure which in turn can determine how easy it is to digest the protein. I cannot think of an example right now; never really checked if two entirely different proteins have identical composition. However, it is not really surprising. In chemistry, it is known that different isomers have vastly different physical properties. 

So if the two proteins have different digestibility then they will have different nutritive values. 

Regarding, protein digestion and nutrition. New proteins are built from individual amino acids and not pre-formed oligomers. Read about translation. So at some point the ingested protein has to be completely broken down into amino acids.