Below are mainly general comments rather than specific to packaging.
SQF has some individual peculiarities with respect to HACCP. Some of these are well documented within this forum. Any relevance may depend on the level of yr technical backup. It also involves the (profitable?) notion of "Practitioner".
SQF allows expansion into quality (=non-safety) topics if required.
SQF provides extremely useful, free, guides except that occasionally the content is disregarded for audit purposes.
BRC tends to adhere more to the classic HACCP references.
BRC offers 2 levels for packaging.
BRC involves further investment if you wish to acquire their "customised" guidelines to Interpretation of the Standard. (true for food, packaging dunno).
But, as already noted, the primary drive may be from the customer side.
Rgds / Charles.C