Hi there,
American Airlines does in fact have a program by which you can switch. You simply get in touch with their customer service department, and send them proof of your elite status. They will review your mileage statements and decide if they will grant you gold status, while at the same time setting a threshold of additional flights within a certain period in which to attain platinum status.
Last year, having gotten extremely irritated with United, included the elimination of the plateau bonuses and other perks for 1K flyers, I contacted American. They granted me immediate status as a gold AAdvantage member, and required that I fly 15000 miles over the next 3 months to achieve platinum status. Good so far.
Now the bad news. Platinum means nothing on American. They will not waive any fees, their upgrade policies are onerous, and service on the flights I've had has been terrible. I just returned from at trip to Paris and it was the worst business class experience I've had. United on the other hand seems to be getting the message that their best customers are mad - I've seen a change since the first of the year. And generally, their planes are nicer, flight attendants are better, and the quality of the service far exceeds American.
I'm glad I tried the switch, if for no other reason than that I appreciate United more.