Importance between the American Mathematical Monthly and Research Journals I am an undergraduate and have been working with one of my math professors over the past year on proving some new results.  These results are interesting and are approachable enough to be understood by most graduate students.  

My professor and I have agreed that this work can certainly be published in a "professional level" research journal (I would be first author), however because the problem is approachable and would be interesting to a wide audience (and is not highly specific) we think it could be a good fit for the American Mathematical Monthly.

I want to go to graduate school, and I am wondering if publication in the American Mathematical Monthly would carry more or less weight in graduate school admissions than publication in a journal specific to the research area of the work (dynamical systems).  

I understand the AMM is geared more towards publishing expository work, however publication in the journal would tend to yield more reads than in a more specific journal (I am looking at the Journal of Dynamical Systems and Geometric Theories for example).  Which would be best to publish in, or look best to a graduate school admissions committee?
You're probably right that more people would see something published in the Monthly than in a "research" journal. But if you are aiming primarily to optimize the positive impact this paper would have on a CV for grad school (in the U.S.) I think it would be much better to say that it has been published in a good-quality research-oriented journal, since that will attest much more strongly to the quality of the research (as opposed to attesting to general interest).

EDIT: in contrast to some other answers' implications... The Math Monthly is not at all a research journal. It is an expository and (mostly elementary) problem/puzzle-oriented journal. Publication there is viewed (in my experience, and in my own opinion) as a good thing, but no indication at all about "research potential" or such stuff. That's not the fundamental criterion for publication there!

So, if you are wanting to give evidence that you have already made (and thus in the future can make) research contributions... publication in the Monthly gets you close-to-nothing. Sure, "it's nice", but it's not at all about making significant new contributions to live subjects. It's an entirely different thing. It's not just "a somewhat different journal"... it's in an entirely different category.