Assuming both file containers had completely unique and strong passwords, are there any benefits or drawbacks to keeping a VeraCrypt (or any other encrypted container) file container inside another VeraCrypt file container?
I'd say it is not worth the trouble. Inserting an additional layer of encryption may thwart the work of an attacker only if he's trying to bruteforce the password, but won't be effective against several side-level attacks (cold boot attack, evil maid attack, malware, etc.). Plus, it will lower dramatically I/O performance as everything needs to be encrypted/decrypted twice.
It would be better to use VeraCrypt in the standard way, concatenating the two strong passwords into an unique, stronger password.