I think that the difference between "identical to" and "identical with" lies in the fact that the former is more commonly used in the UK and the latter is more commonly used in the USA. Being of British nationality and a teacher of English in China, I believe that the following are correct and acceptable:

Be identical to
Be equal to
Be similar to
Be different to/ from
Be the same as

The prepositions "to" and "with" have varying implications according to the context in which they are used. Here, "to" implies "in relation to", whereas "with" implies "in relation with".