As Doctor Grant says of the dinosaurs in
Jurassic Park, Latin never did die; it evolved into something else. The sort of Latin we have records of is almost solely upper-class literary Latin. There's graffiti in Pompeii which is in the vernacular, and some of the Classical authors use lower class formations consciously to evoke a particular milieu. Ooh, that sounded pompous!
We're very lucky with Ancient Greek to have a few splendidly lower class sources from 2,000 years ago that we can compare to the high-falutin' stuff. I refer, of course, to the New Testament. Latin's a less fluid and evocative language than Greek, incidentally, and it's still changed considerably from Ancient Greek. e.g.
stasis in Ancient Greek means
political turmoil or even
civil war. In modern it means
bus stop. That said, one can make oneself understood to modern Greeks if one doesn't mind speaking slowly and having them wonder why one's mispronouncing everything.*
* In modern Greek epsilon, eta and alpha+iota are all pronounced
e as in b
et. It's almost certainly one of the reasons for Greece's poor showing in literacy tables.