Citing contemporaneous (interlaced?) preprints

Cite relevant literature

Since you have the option of adding a citation to a relevant source, you should do it. It improves the paper by making it a more useful reference, and comparing and contrasting the results might also be useful.

Priority

If relevant, use a phrase like "A very recent preprint A claims this and that.", or even, if your results are very similar and you really need to emphasize priority, "During peer review of this article a preprint A was published. The preprint...".

Who is in the right matters somewhat less than who is in control. Refusing the request of a referee possibly leads to rejection of the paper.

But you may not need an extended discussion of the other paper, but a notice that it exists and is related in -whatever- way. This is simply a service to readers who find one paper and are interested in the topic generally.

You seem to be insisting on a claim to primacy here, which may not be completely warranted. The work on the two papers, and the key insights, occurred more or less at the same time - independent research. The fact that one hit the streets a bit before the other is less important than that certain problems were solved and some questions have been answered. The earlier date of issue could occur for any number of random reasons. Had it gone the other way, how would you feel?

Citations are not simply for listing the papers you referred to while doing the work. "We didn't use this while writing the paper" is not a reason to not cite relevant material. Besides, you haven't even finished writing the paper – it's still being revised!

Whether or not the new paper requires a detailed discussion depends on its relation to your own. You should discuss it as much as you would if it had been available before you submitted your paper.