IMHO, JSON Feed is basically irrelevant: It adds little to no functionality, development seems to have stalled after a short initial burst of enthusiasm and as far as I know nothing supports it but not Atom.
Atom is technically superior to RSS, most concretely in how it specifies the format of fields like title and content, whether they’re plain text or HTML. This means that I can use things like <em> and <code> in my blog post titles and have it work (clients will either display the HTML unaltered, sanitise it, or strip tags, leaving the correct text), and have blog post titles with text like <_>::v::<_> (real example!) not get mangled horrifically.
I do not recommend that anything use RSS now.
I would also encourage Atom over RSS, the specification is simpler and less ambiguous.