Actually, the takeaway I had was that the Roman artifacts were precious and would be taken seriously, whereas the Byzantine artifacts were considered disposable.

I suspect this happens for two reasons. One is that the Byzantine era, being later and more prosperous, simply has more artifacts and is more well-understood, so new finds are less interesting. But I suspect the bigger reason is that the Roman Empire has a better reputation in history as the glorious pinnacle of Western Antiquity whereas the Byzantine Empire is denigrated as 1000 years of stagnant decline (although neither of these characterizations are very accurate).