One drawback of creating private method in Javascript is memory-inefficient because a copy of the private method will be created every time a new instance is created. See this simple example.

function contact(first, last) {
    this.firstName = first;
    this.lastName = last;
    this.mobile;

    // private method
    var formatPhoneNumber = function(number) {
        // format phone number based on input
    };

    // public method
    this.setMobileNumber = function(number) {
        this.mobile = formatPhoneNumber(number);
    };
}

When you create few instances, they all have a copy of formatPhoneNumber method

var rob = new contact('Rob', 'Sanderson');
var don = new contact('Donald', 'Trump');
var andy = new contact('Andy', 'Whitehall');

Thus, would be great to avoid using private method only if it's necessary.