The only actual benefit I can find where business cards differ from personal cards is that the card's car rental coverage benefit is primary, although only on business rentals. On personal rentals or on all rentals on personal cards, it is secondary to any existing insurance you may carry.

From what I've been able to tell, there's not much of a difference between a personal credit card and a business credit card for a sole proprietor. If you have a company with multiple employees, business accounts have some additional options--for example, some (but not all) business cards allow you some flexibility to give different cardholders different credit limits or track charges to different cards on the statement (whereas additional cards issued on personal accounts typically share a card number and don't appear segregated on the statement). Also, I believe it is possible for a business card to be applied with the business's tax ID number instead of the applicant's social security number, which bases the application on the company's business credit history (though it's handled through different credit bureaus, like D&B, rather than Experian et. al) rather than the individual's credit score.

The AS business Visa also allows the company to choose whether they want to receive miles in a single account for all cardholders or whether each cardholder should receive their own miles for their own purchases.

As mentioned above, best scenario (if you qualify): get one of each and then you have two companion fares! (And no, I don't think additional business cardholders get their own separate companion fares...)