The verdict
If you are testing an idea, collecting a waiting list or selling one thing, pick Carrd. It gets a clean page live the same day, and the cost of a wrong idea stays small. If you have a real catalogue, repeat customers or business buyers with their own price lists, pick BigCommerce.
They are also not exclusive. Carrd works well as a place for tests and campaign pages beside a larger site. The mistake I would avoid is forcing a one-page tool to act like a shop, or buying a full store before you know anyone wants the product. Start with the page. Move to a store when orders create admin you cannot handle by hand.