Do I need to cite a working paper that was written after I wrote/presented my manuscript? I need some help deciding how to cite a paper that is rather similar to my own. I wrote a paper in Nov 2017 and presented it at conference that year when I was 8 months pregnant. Then I went and had a baby. I didn't submit it, because I was a bit overwhelmed and I felt like noone else was doing work on this problem so the paper was "safe." (I didn't get maternity leave so I just had to keep teaching my full load with a newborn - not something I would recommend.) 

I presented a follow-up paper at Nov 2018 conferences and one of the other papers on my panel was VERY similar to my 2017 paper. It seems somewhat like an extension of my work, although they were not aware of my work. (Which seems a bit ridiculous because we go to overlapping conferences.) At least one of the authors on the other paper is senior/famous. 

Now, I am pushing hard to submit my 2017 paper to an Economics journal this month. How should I cite/discuss their paper? Right now, I am leaning toward not talking about their paper but instead putting a note about their work in my comments to the editor and letting the editor decide how it should be included.

Since seeing my 2018 presentation, they added the following to their paper's conclusions: "During the course of writing this paper, we became aware of a working paper that [general topic] (see ...). [Then they explain in two sentences how their work is distinct, of course making my work sound a bit more basic than theirs.]"

Do I need to do something like this in my text? It feels a bit unfair since I demonstrably had the idea first.
Asking your editor is a good solution to an unusual situation. You could also include a note at the end of your paper citing the more recent work and giving an explanation that is complementary to the note in the other paper. 

But someone who reads either of the papers would want to be apprised of the other, so the citation would be useful to researchers. 

I think the priority of your work is clear, from what you say, and is recognized by the other authors, so there is no reason to disguise or omit any information.