There is no such thing as "objective" in this arena. It's all subjective, the best you can hope is to find an approach that the majority of your users subjectively prefer.
It’s not a “which payment” window though, it’s a “confirm payment information” window.
In that type of window you’d expect clicking on any of the existing form fields would allow you to change that field. It would be wild if clicking on a credit card icon in the middle of a form submitted that form.
There is no such thing as "objective" in this arena. It's all subjective, the best you can hope is to find an approach that the majority of your users subjectively prefer.