Unpublished paper with published followup gathers citations: should it be published? A few years ago I wrote a paper with three collaborators, where we introduced a model to describe a specific phenomenon. In the end we were not fully happy with the result, so we wrote it up, put it on the arXiv without submitting to a journal, and agreed to revisit the subject after a small break.

Approximately a year later we gathered again, re-started almost from scratch, and came up with a better model, which resulted in a paper that we quickly submitted, and had accepted in a good journal.

A bit more than a year later, I now see that even though the second paper gets cited, the first still rakes up some amount of citations. We ourselves think that the second one is better, but obviously there are people who disagree. 

What to do with the first paper? Should it be submitted to a journal to undergo peer review? And would it not be strange to try and submit the first paper to a journal, pretending that the second paper never happened?
I see no reason that you really need to do anything with the first paper. In arXiv it is a stable, citable resource, people are finding it useful, and the citations are accruing credit to your work.

If you are concerned that people who are reading the first paper are unaware that it is obsolete, then you can add update its entry to add a pointer to the second paper. People will still likely continue to cite the first paper, however, either because they have reason to prefer it or because it's already in their reference collection and they don't revisit and see your update.

Other than providing a pointer to the second paper, though, I see no reason not to just let well enough alone, be grateful the people are appreciating your work, and move forward onto other things.