I hope this example help for you
Apart from .diff(), you could also use moment durations: http://momentjs.com/docs/#/durations/
Example Fiddle: https://jsfiddle.net/abhitalks/md4jte5d/
Example Snippet:
$("#btn").on('click', function(e) {
    var fromDate = $('#fromDate').val(), 
        toDate = $('#toDate').val(), 
        from, to, druation;
    from = moment(fromDate, 'YYYY-MM-DD'); // format in which you have the date
    to = moment(toDate, 'YYYY-MM-DD');     // format in which you have the date
    /* using duration */
    duration = moment.duration(to.diff(from)).days(); // you may use duration
    /* using diff */
    //duration = to.diff(from, 'days')     // alternatively you may use diff
    /* show the result */
    $('#result').text(duration + ' days');
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.11.1/moment.min.js"></script>
From: <input id="fromDate" type='date' />
To: <input id="toDate" type='date' />  
<button id="btn">Submit</button><hr />
<p id="result"></p>