Well, the first thing you need to remember is that you can only recover from pots what you carry in pots. This is an obvious point, but important in its implications, because in many respects a pot is a terrible transport vessel. They are difficult and time consuming to create an require considerable skill on the part of the potter and a particular set of resources. And once they are done, they combine heaviness with fragility.

What this means is that you only carry in pots what you need to carry in pot, which are the cools that require the extreme impermeability of ceramic. Liquid goods, such as wine and plant oil, and obvious choices, but also grain, as the small grains can leak through the gaps of woven sacks. Siphilim, on the other hand, was a reed, and was much more likely to be transported in bundles that are easier to transport and do not require the labor and resources involved in pottery.

In terms of modern recovery, it is overwhelmingly limited to liquid goods such as wine, oil and sauces. Liquid goods are most favorable because they leave a residue on the inside of a vessel that is much more likely to survive than a few loose grains.

I can source specific claims here, but most of this answer comes from personal experience in archaeobotanical research.