I am not a chemist, but as it's been explained to me by some very brainy cats here, the following is true:
Presuming the OP means conventional = grp II or II+, and "full synthetic" means grp IV (PAOs) ...
Yes, there is something that conventional oils do better than "full syns", believe it or not.
PAOs are not nearly at good at keeping additives in suspension; Grp II and II+ and III are much better at doing so. In fact, it is very common to see a hint of conventional oil mixed in with a "pure" PAO, so that it can carry the additives. There's no such thing as a "pure synthetic" (most commonly thought of as PAOs), because if it were "pure" there'd be lower base stock to carry the additives.
Now, if you are willing to accept that Grp III is a "full synthetic" (which many are not), then the conversation turns a bit because Grp III syns can carry their own additives well.