Moment.js is a fantastic library, so it is nice to use a library which sits on top of it. Twix.js should do the job for your needs.
http://isaaccambron.com/twix.js/
From the "Smart Formatting" section on that page:
moment("1/25/1982 9:00 AM").twix("1/25/1982 11:00 AM").format(); //=> 'Jan 25, 1982, 9 - 11 AM'
moment("1/25/1982 9:00").twix("1/26/1982 13:00").format(); //=> 'Jan 25, 9 AM - Jan 26, 1 PM, 1982'
It looks like there are plenty of modifiers you can use, so that if you are more concerned with time-ranges rather than date-ranges, you can omit the day portion of the resulting string.