How much more regular and simple the grammar is, compared to Ancient Greek. Downside: extensive borrowings from Ancient Greek have messed it all up again.
The bits of Latin, Venetian, Turkish, Slavic, and even Catalan in the vocabulary, that show you how Greek history did not end with Alexander. Downside: a lot of these have been whitewashed.
The subtle variations in emphasis that come from free word order, that isn’t used just to fit the metre in poetry. Downside: reading a one size fits all word order in journalistic and prosaic Modern Greek.