One approach to test the effectiveness of a translator is translating a passage from L1 to L2 and then its reverse. When you do this action many times, if the final version of the passage in L1 gives the meaning of the original passage in L1; then it is a stable translator. They do this test for English-German at Linguee translator. Their claim is that it is more successful than Google translate in these terms. This gives another idea that Google Translate does not give strong results for English-German translations. Considering German is much more closer language to English than Turkish, I don't expect much from Google Translate. Thus, I don't see it as a proof to any argument.
Computers cannot deal with the ambiguities of Turkish. That says nothing about English being superior to Turkish.
However, not having a central controlling authority and not having gone through censorship drives, English does have a much richer vocabulary in common daily use to more specifically express various subtle distinctions whereas a Turkish speaker has to rely on context that is not embedded in the grammatical structure and specific words used.