Who faces more difficulty, a Greek who reads the original Koine New Testament or an English speaker who reads the works of Shakespeare?

How on earth do we quantify this? Especially given (a) we read Shakespeare in modernised orthography; (b) we ignore the pronunciation differences, unless we’re tuning in to Ben Crystal for Reconstructed Shakesperian, and Randall Buth for Reconstructed Koine; (c) there is huge stylistic disparity in the New Testament: Mark is much easier to read than Paul.

• Pronunciation: Koine slightly harder: the vowels sound like a pirate in English, but we have heard pirates before in the movies. Greeks are going to be really taken aback by eta as /ɛ/ and omicron iota, upsilon as /y/; but they’re getting off easy. Those are the only real differences.
• Morphology: A lot of Koine grammar got reintroduced to modern ears via Puristic (I’m saying that deliberately: Puristic never really used pre-Koine Attic grammar). Still, that’s an alien though familiar grammar for Koine, vs only minor grammatical differences for Shakespeare.
• Syntax: Same as morphology, although Shakespeare’s syntax can at times be convoluted for modern ears. I’d call it a wash.
• Lexicon: This can be quantified, but I don’t know of any studies. Both are contaminated, because of how canonical both are in the contemporary cultures: the vocabulary of the New Testament and of Shakespeare are more familiar to modern readers than they should be, because both are taught (and because of Puristic). And you’ll need to be “edified by the margin” for both. Especially if you used an edition of Shakespeare that uses the word margent instead of margin. I’m calling it a wash, but more out of frustration than conviction.

Koine somewhat harder than Shakespeare, but I say that with little conviction. Koine maybe as easy as Chaucer. But certainly easier than Early Middle English, from what little I’ve seen of it.