if someone is storing the data for you, you are pretty much locked in. spending the extra time and managing the data yourself is probably a really good idea.
That's true for everything except credit card data. If you have to ask, storing users' credit card data is almost always a bad idea. The information is very sensitive, and any compromise is very serious. That's why if you store payment information, you generally have to implement a number of best practices to achieve "PCI compliance". This costs you time & money, as well as additional policies and regulations at your company. Unless your revenue is reasonably significant (say, over a million per year), it's probably not worth the hassle. Outsource your payment processing.