Is there a big difference between Modern Greek and Medieval Greek?

Non-zero, but not huge.

Mediaeval Greek is  not the normal term used, because the Greek linguistic situation doesn’t align well with the Middle Ages. Let me explain.

The learnèd language of Byzantium was Attic Greek, with varying degrees of enthusiastic hypercorrection and exoticism. The officialese language of Byzantium was closer to Koine, with plenty of Latin terms.

The vernacular language is not well attested. We have the papyri up until around 700, a couple of generations after the Arab conquest of Egypt—although they represent one region and what was often a second language. Our first vernacular texts are from the mid 12th century, but all vernacular literature is macaronic with more archaic Greek, up until at least the Cretan renaissance.

Betweem 700 and 1150, we have some acclamations and ditties from chronicles, and the Proto-Bulgarian inscriptions, likely written by Greek POWs.

Received wisdom is: the Greek vernacular switched from Middle Greek to Modern Greek  in the Dark Ages—so around 1000.

The pronunciation of Greek, at a phonemic level, was pretty close to Modern by 500; the final change, of οι and υ to /i/, seems to have been around 1000 (a poem makes fun of the new pronunciation in 1040; but these things always take longer—place name evidence shows the old pronunciation lingering for another century). I’m not sure we know when double consonants were degeminated—and of course they haven’t degeminated in all Greek dialects.

The morphology seems mostly modern by the start of Early Modern Greek. The dative and future tense is still to be seen in the bits between 700 and 1150, but is gone by the first Early Modern texts. Verb tenses took a while to settle down: the future particle θα is 17th century, and the volitive future it came from (θέλει Verb) is 14th century; the perfect is 17th century, the pluperfect even later; the conditional used to use the aorist instead of the imperfect (να είδες, not να έβλεπες). The positioning of clitics was not the modern positioning; as with other features of Early Modern Greek, it was closer to Modern Cypriot than to Standard Modern Greek.

So the differences between 1200 Greek and 2000 Greek are noticeable. But I have to say, they’re not huge. The vocab is a bit on the exotic side; but within the range of modern dialect. If I were to compare it to English, maybe Shakespearean English, maybe later. (The tense “was being built” after all is only 19th century in English.) If you have some linguistic smarts, you’ll understand it just fine.