It's generally easier to manage a proper resume tailored to each company with a well-structured LaTeX file than with Word. If you want to specifically draw attention to the fact, just toss \LaTeX into skills, though, honestly, most of us familiar with LaTEx can recognise a lot of distinguishing characteristics that few people bother to change.

If the person receiving the resume doesn't know what LaTeX is, they still have a relatively portable format and you expended less effort getting it to them. Win/Win.

For me, LaTeX is the simplest way to make a decent-looking PDF with minimal fuss. It's no more work than putting up an HTML CV.

I agree with the other commenter, using LaTeX has nothing to do with impressing the reader with my (shallow) LaTeX skills, and everything to do with not having to deal with something like InDesign or whatever other painful WYSIWYG tool most people use for this kind of thing.