I am a member of both. And Costco does not let you use coupons, the items here seem to be in a larger bulk quantity. At Costco's you also can only use cash, debit, or American Express. You also need a costco card to enter.
At BJ's you can use coupons, they offer coupons at the door, and they frequently have great instant rebates. You can enter a BJ's without a membership card, you can actually purchase items to but at a higher price.