That depends, in part, on how you measure similarity. In most respects, it would be closer to Classical Greek. The lexicon wouldn't have had any influence from Slavs or Turks, who hadn't arrived in the region yet. Justinian's education in Constantinople would have rendered him literate in, if nothing else, the 5th century Attic dialect, and would presumably have an 'atticizing' influence on his idiolect.

Phonology, however, would have been markedly different from Classical Greek. Distinctions in vowel length (a la Latin) had been lost and the pitch accent had evolved into a stress accent. Most diphthongs had shifted into single vowels, though not necessarily to their modern values. αυ and ευ would be approaching their modern values of 'af' and 'ef', and the consonants would generally sound like they do in modern Greek (e.g. βασιλευς and θεος would be 'vasilefs' and 'theos' not 'basileus' and 'teos').

Structurally, and on paper, the language would probably look more like Attic. Hearing it, especially if you were only paying attention to the sound and not the words, it would probably sound a lot more like modern Greek.

Justinian was the last emperor to speak Latin, though I believe in a barbarized form. Generally, however, modern Greek derives from the Hellenistic and medieval koine, not from classical Greek.

I did not mean that Justinian's Latin was "bad" any more than French or Spanish is bad Latin, just barbarian in the sense of not Roman. Language evolves. I recall seeing the term self service "misspelled" in Istanbul. Then I realized that the term had entered the Turkish vocabulary and that the Tuirks were entitled to spell it any way they wanted.