If all your data exists in a file hierachy that you can browse, edit manually, and back up, then you have the safety of relying only on foundational systems for the survival of your data, and the power to use your data as you please with tools of your choosing. But if the application owns your data—if it stores it behind the scenes and never exposes it to you directly—then your data is exactly as fragile as that application. If there’s a bug, your data can disappear. If the company goes under, your application can rot to unusability. If the product is discontinued, the same. If the company kills a feature, you have to do without it. Or, most likely of all, the company could start publishing buggier and buggier updates, and you’ll have no choice but to use buggier and buggier software.
It seems like a clear choice to me: if the data is anything I value, I must have direct access to it, regardless of what tools I use to manipulate it. The only data I let websites or applications own is data I’d be OK with losing.