With momentjs, how do I tell if 2 moments represent the same day (not, necessarily, the same time)?

You can use both 'day' and 'date' to isSame.

As the docs says:

Check if a moment is the same as another moment.

When including a second parameter, it will match all units equal or larger. Passing in month will check month and year. Passing in day will check day, month, and year.

Like moment#isAfter and moment#isBefore, any of the units of time that are supported for moment#startOf are supported for moment#isSame.

In the docs of startOf:

Note: moment#startOf('date') was added as an alias for day in 2.13.0

Here a working example with the lastest version (2.17.1):

var moment1 = moment('01/23/17', 'MM/D/YYYY');
var moment2 = moment('01/23/17', 'MM/D/YYYY');
console.log( moment1.isSame(moment2, 'day') ); // true
console.log( moment1.isSame(moment2, 'date') ); // true

<script src="//cdnjs.cloudflare.com/ajax/libs/moment.js/2.17.1/moment.min.js"></script>

Let's keep it simple.

moment(date1).format('L') === moment(date2).format('L')