It all depends on the issuer. To most of them, a large number of inquiries in a limited time is proof of risky behavior. I would look at which bureaus have what number of inquiries and focus on the one with the least. Credit Pulls Database can help you determine what banks pull what reports going forward.

To avoid hard pulls, some lenders like AMEX, don't hard pull for new accounts for existing customers. Navy Federal there are ways to get soft pull cards at certain times of the year.