VP is the Manager grade. It wouldn't make much sense to stay (with less compensation) for a promotion to Manager which isn't even guaranteed, and lose the opportunity to move out into the same level role, at the very destination you'll want after promotion to Manager at Big 4 anyway.
Big 4 - Bank VP - ? makes you more marketable than Big 4 - Manager Big 4 - Bank VP
You would still be moving across at VP level even if you had already won the promotion to Manager within Big 4 anyway, so go for it.