I think you're more protected in the browser. On iOS any app can access the clipboard without having to ask for any permission.
The encryption scheme on iOS is nice, but for how much of a game they talk about privacy Apple had the opportunity to do so much more for security around identity/auth and they did approximately nothing.
Because you usually don't have control over that. On lots of system, any application that can display an UI can access the current clipboard's contents.
Taking a step back from the problem, users do usually have some amount of control over what is running on a system.
I mean, I understand that computers managed by typical users will be a shitshow, but much of the problem in that situation is that they don't really care.
I believe the browser is one of the few applications that already take this into account, fortunately. Clipboard access from Javascript is secure, for example.
The encryption scheme on iOS is nice, but for how much of a game they talk about privacy Apple had the opportunity to do so much more for security around identity/auth and they did approximately nothing.