If you are only interested in checking if dates occur on the same day regardless of time then you can use the toDateString()method to compare. This method returns only the date without time:
var start = new Date('2015-01-28T10:00:00Z');
var end = new Date('2015-01-28T18:00:00Z');
if (start.toDateString() === end.toDateString()) {
// Same day - maybe different times
} else {
// Different day
}
var starDate = moment('2018-03-06').startOf('day');
var endDate = moment('2018-04-06').startOf('day');
console.log(starDate.isSame(endDate)); // false ( month is different )
var starDate = moment('2018-03-06').startOf('day');
var endDate = moment('2018-03-06').startOf('day');
console.log(starDate.isSame(endDate)); // true ( year, month and day are the same )