I've moved a few businesses off of Stripe and never had any problem. They do it with PGP keys and go directly to the new provider so I never touch any info. Worked great.
You moved them from Stripe to where and why? I'm about to launch a product in a few months and trying to decide which company to go with. So far Stripe seems to be most favorable for the development team. But maybe there are some business things that make Stripe less desirable. Thanks for any insight.