How to compare only date in moment.js

The docs are pretty clear that you pass in a second parameter to specify granularity.

If you want to limit the granularity to a unit other than milliseconds, pass the units as the second parameter.

moment('2010-10-20').isAfter('2010-01-01', 'year'); // false
moment('2010-10-20').isAfter('2009-12-31', 'year'); // true

As the second parameter determines the precision, and not just a single value to check, using day will check for year, month and day.

For your case you would pass 'day' as the second parameter.