Report blatant self-plagiarism to journal editor or PubPeer?

Taking the complaint public shames both the author and the journal, which may be counterproductive if the journal is responsible and willing to act promptly (mistakes do happen, even for very good journals).

I would thus recommend starting by reporting to the journal, which should have a procedure for dealing with such things. If the journal does not take you seriously or refuses to act, then take it public and shame both the author and the journal.

I suggest that you report this to the journal or editor first. If they fail to properly react to it, you can still escalate this by making it public. While the journal is likely to blame for not using proper plagiarism detection mechanisms, they are also likely the victim here, not the culprit.

Also, keep in mind that there may be reasons for this duplicate publication, e.g., one of the papers being published at a predatory publisher (see also this question which is essentially the same situation happening to a peer-reviewer).