I mean, this dips into the whole issue of how to quantify and measure diversity, and so on. But I would like to challenge the basic assumption behind your question. Let's consider an area that's approximately the size of Europe: Greater Iran plus The Indian subcontinent. This also presents what I would consider a fair mixture of densely and sparsely populated areas, and so on.

Here you have: speakers of the full range of two major Indo-European branches (Indic and Iranian), speakers of the full range of all Dravidic languages (Telugu, Tamil, etc); both of which have huge amounts of internal diversity, several Turkic groups, and so many minorities it would be futile to even attempt to count them. In terms of religion, you have large groups of several schools of both Sunni and Shia muslims, just about every conceivable brand of Hinduism, as well as minorities practicing Buddhism, Jainism, Zoroastrianism, Christianity, and so on. You will find the heritage of any number of empires ancient and modern.

By any number of measures, this region is at least as culturally diverse as one could conceivably construe Europe to be. And this, obviously, is hardly the most diverse area I could've picked - you could look at the Transcaucasus, about half the size of Germany, containing local majorities from three different language branches (Georgians, Armenians, and Azeris). Or at Southeast Asia with the mixture of Mon Khmer, Malay and Thai languages, and many different religions.

None of these are any perfect measures of cultural diversity, of course, but it is certainly not obvious to me that Europe would be more diverse in any sense I can think of. It is overwhelmingly Christian, dominated by speakers of one of three Indo-European language branches (Romance, Germanic, Slavic), plus a sizable population of Turks, and various diasporas and minorities. This seems very comparable to any other area of similar size to me.

Maybe there's some aspect I've missed that you could specify?