Ironically, the cards with the least chargeback risk (corporate purchasing cards) actually cost our firm the highest rate (non-qualified, same for anything with a business name embossed on the card). We have negotiated exceptionally low rates on American Express (we have a picture of our sales rep in an unsavory position), so we pay below 2%, which is quite unusual.
American Express frequently targets some market segments for better discount rates; we see this especially in grocery and hardware - I suspect there may be some logic there, as people who use their cards at grocery and hardware stores may tend to carry a balance and generate finance charges, which is where the real money is made.
Eric