Moment.js can't handle this scenario directly. It does allow you to take the difference between two moments, but the result is an elapsed duration of time in milliseconds. Moment does have a Duration object, but it defines a month as a fixed unit of 30 days - which we know is not always the case.
Fortunately, there is a plugin already created for moment called "Precise Range", which does the right thing. Looking at the source, it does something similar to torazaburo's answer - but it properly accounts for the number of days in the month to adjust.
After including both moment.js and this plugin (readable-range.js) in your project, you can simply call it like this:
var m1 = moment('2/22/2013','M/D/YYYY');
var m2 = moment('4/5/2014','M/D/YYYY');
var diff = moment.preciseDiff(m1, m2);
console.log(diff);
The output is "1 year 1 month 14 days"
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