These schools have quite different campus cultures. Williams has long been a desirable destination for kids from New England prep schools, and it retains that “feel” of tradition and privilege in spite of having greatly diversified its student body. It is an athletic powerhouse in a very competitive D3 athletic conference and has a lot of student athletes. The academics are excellent and the students are serious about their studies. It is a school that feeds highly selective companies in IB and consulting… The tutorials are a true differentiator.
Grinnell is very well resourced and draws much more heavily from the Midwest. The student body tends to be less traditional and takes some pride in that. With that said, there are, at both schools, students who would be more the “type” for the other.
I think that this is really more a matter of dominant culture, and if you are the person who is happy with your friend group and somewhat oblivious to what everyone else is doing, this may matter less.
Williams is significantly harder to get into. Unless you are hooked, it IS a reach, not bordering on it. I would take a look at your expected course of study and see how it looks at both and if any of the differences push you strongly in one direction or the other. While I am not a huge fan of sites like Niche for this, reading through comments there might give you a sense of what you want to probe.
They are both excellent schools.