As you have already mentioned, there are two approaches to FA token burn implementation:
1) Transferring to "burn address".
In this case you don't really burn tokens, but just send them to a random valid address that supposedly no one has access to, so they supposedly cannot be accessed anymore.
- no need to implement a "burn" entrypoint.
- transfer operation spends more gas, because it updates 2 balance records in contract's storage, instead of just one;
- transfer operation spends extra storage, because when it sends a token to a burn address first time, in writes a new balance record
(burn_address, token_id) -> balance to contract's storage;
- complicated supply calculation, because "burned" tokens still exist, especially when people use multiple different burn addresses (nothing stops them from doing so);
- there is no 100% guarantee that really no one will ever get access to the burn address, despite the fact that this is almost impossible :D
2) Removing from contract storage.
In this case you simply decrease or even remove someone's balance from the contract storage, that means that tokens are really burned.
- doesn't spend extra gas (i.e. less baker fee);
- doesn't spend extra storage (i.e. less storage fee);
- simple supply computation (just a sum of all balances);
- there is 200% guarantee that really no one will ever access burned tokens :D
- you will need to implement a "burn" entrypoint.
So, removing tokens from the contract storage is the best approach, IMO.