You can certainly get both the biz and pers Starwood Amex. I got 'em both in my wallet right now.
As to the advantages of the biz card. Zero. Except for the additional bonus Starpoints. @:-)@:-) @:-)
The pers card is better because it is protected by the Federal Fair Credit Billing Act--biz card is not.
I always use a pers card over a biz card unless there is some very good (miles bonus) reason to do otherwise. And, if I think there is the slightest chance there could be a problem with a charge (think car rental in Spain) I always, always use a personal Amex card, never biz. Although I am thinking about starting to use my Schwab pers card due to better exchange rate.