In short, yes, include links to both versions on both URLs.
The hreflang attribute is used as a signal to help search engines offer a specific version of your website in search results. Observant visitors will expect the content to be in their dialect of English (British English, American English) but that's beside the point.
Google's Webmaster Tools has an excellent resource on the topic that addresses your case.
It's a good idea to provide a generic URL for geographically unspecified users if you have several alternate URLs targeted at users with the same language, but in different locales. For example, you may have specific URLs for English speakers in Ireland (en-ie), Canada (en-ca), and Australia (en-au), but want all other English speakers to see your generic English (en) page, and everyone else to see the homepage. In this case you should specify the generic English-language (en) page for searchers in, say, the UK. You can annotate this cluster of pages using a Sitemap file or using HTML link tags like this:
<link rel="alternate" href="http://example.com/en-ie" hreflang="en-ie" />
<link rel="alternate" href="http://example.com/en-ca" hreflang="en-ca" />
<link rel="alternate" href="http://example.com/en-au" hreflang="en-au" />
<link rel="alternate" href="http://example.com/en" hreflang="en" />