I would not recommend blindly updating the libraries as there have been significant changes.
Storage client library 2.0 (which is part of SDK 2.1) is drastically different (though much better IMHO) from previous versions. There have been namespace changes, some methods were removed.
Diagnostics libraries in SDK 2.1 have a dependency on Storage Client library 2.0. Again, I would not recommend upgrading that either.
My recommendation would be to evaluate the impact of upgrading libraries from 1.6 to 2.0. Please go through the following blog posts by storage team:
I also wrote a series of blog posts on upgrading code to 2.0 version which you can read here:
http://gauravmantri.com/2012/11/17/storage-client-library-2-0-migrating-table-storage-code/
http://gauravmantri.com/2012/11/24/storage-client-library-2-0-migrating-queue-storage-code/
http://gauravmantri.com/2012/11/28/storage-client-library-2-0-migrating-blob-storage-code/
http://gauravmantri.com/2012/12/26/storage-client-library-2-0-exception-handling/
http://gauravmantri.com/2012/12/30/storage-client-library-2-0-implementing-retry-policies/