Hi Alexander,
Please check whether subscription center of your current content setting is same to marketing page url of 2nd link.
e.g: We may have multiple content settings.
In my environment, the "Default Content Settings" will be set to Content settings field of customer journey by default,
thus to use my own subscription center(an external page), I need to switch to "My Content Setting".

If I don't change it, then both links will lead me to same page.
(It seems that embedded form was not associated with an URL, so could you tell me how did you add 2nd link via marketing page?)
If above is not your situations, you could also try attach the link to text directly.

Both of my subscription center forms are embedded on my own external website, and the form of page 2 will still be prefilled if I open it via the link in email.
page 1

page 2

Regards,
Clofly