Kseniia, Maybe I'm confising it with another phrase, but I remember once I googled for it and found that какая разница между is even more common in google.
I didn't bother to check ruscorpora (maybe I will) but I suspect that in 19th century literature "какая разница" must be even more common (French "quelle est la difference"... cf. also "со многими ошибками" less common now, with an adjective where we now don't use one). And I don't know how "какая" worked in 18th century before the French influence.
So my reasoning was that, if a half a country is using a form and literature likely also is using this form (and our classics is still the basis of our literary language much more than in English), then its MY usage is "regional". Even if my region is "Moscow". Since my cousin (3d cousin) from Novozybkov came to Moscow determined to get rid from her very musical intonations and learn to speak "properly" I'm fiercely opposed to the idea that Moscow dialect is "more correct":)
какая разница между: 1775-1900, 62 examples.
в чём разница между: before 1917, 1 example (someone Leo Tolstoy)
As I said, Russians are different in that we read our 19th century classic literature in huge amounts and call what we speak "literary Russian". Some forms (not many) aren't used but aren't considered a mistake too.
When something is used in classics AND in modern times...