People shop a rented shipping container against a branded moving pod and assume they are the same. A shipping container is a bare 20ft or 40ft steel box you arrange transport for. A moving pod is a managed service with delivery, storage, and transport built in.
Verdict: A moving pod for almost every household move, because delivery, storage, and transport are handled for you. A bare shipping container only if you have your own hauling plan and want maximum space for the lowest raw cost.