According to several grammatical sources (including previous editions of the MGMAT SC guide), both usages are considered correct. However, In my personal experience as a native speaker of American English (from which the GMAT derives its idioms), I can tell you that "identical to" is much more common, and "identical with" sounds strange to my ears.

There is no instance that I can find of this idiom being tested on the GMAT, however. Please let me know if you come across an example from an official source. Thus, it's probably unlikely that you would encounter this issue on the GMAT. If you did, it's likely that either one would be considered correct.