You can use entropy if all the proteins you test are found in the same species, if you use different sets of species your measures will not be comparable between two proteins.

You can use the phylogenetic tree to obtain a conservation score which will be more accurate and even comparable to amino-acid conservation. An example for a tool that computes the rate of change of amino acids is rate4site, you can change the matrices to use it for the turn types. The output of rate4site will give you the rate of change for each turn and the results will be compared between proteins even if they are found in completely different species (assuming you believe the phylogenetic tree)