How user could go into a page with out log in to ? I have never seen any major website use pop up for log in ; i think one of main reasons ; it's not accessible. but if are looking to find a solution that user don't leave the page , you could go for drop panel .
I agree that both are beneficial, but a separate login page is essential. The reasons for having a login page on it's own page shouldn't just be to "declutter" but rather it should be decoupled in the case where a "users" primary task(s) have to do with logging in. I think the pop-up works but should be carefully considered, if the login is "in the way" of ...
Often times you need both. The pop up sign in (or a drop in panel) is the smoothest experience for most use cases. It allows users to sign in without leaving their current path. But you will also run into cases where you need to land users on a sign in page. In my experience, this should be the exception, not the standard. One example of the exception ...
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