What is the correct way to check for string equality in JavaScript?

You can use == or === but last one works in more simple way (src)

a == b (and its negation !=)

a === b (and its negation !==)

String Objects can be checked using JSON.stringify() trick.

var me = new String("me");
var you = new String("me");
var isEquel = JSON.stringify(me) === JSON.stringify(you);
console.log(isEquel);

Strict Comparisons

To do simple comparison, use === to check for strict equality. As others stated, this has the advantages of being most efficient and reducing the chances of buggy or uncertain code. Source: MDN Web Docs: Strict Equality.

var a = "hello1";
var b = "hello2";
console.log("a === a?" + (a === a) + "|");
console.log("a === b?" + (a === b) + "|");

Alphabetical Comparisons

If you want to compare two strings to know if a string comes before or after another string, based on natural sorting, use the <, >, <=, and >= operators. Source: MDN WebDocs for <, >, <=, and >=.

    var a = "hello1";
    var b = "hello2";
    console.log("a < a?" + (a < a) + "|");
    console.log("a < b?" + (a < b) + "|");
    console.log("a > b?" + (a > b) + "|");
    console.log("b > a?" + (b > a) + "|");

Considering that both strings may be very large, there are 2 main approaches bitwise search and localeCompare

I recommed this function

function compareLargeStrings(a,b){
    if (a.length !== b.length) {
         return false;
    }
    return a.localeCompare(b) === 0;
}

Also consider that ["foo", "bar"] == "foo,bar".

For strings, we have a supported method localCompare which is very handy in string comparison. IMO, we should just use it and doesn't need to complicate stuff.

Usage:

const a = 'Hello'
const b = 'Hell'

a.localCompare(a) // 0
a.localCompare(b) // 1
b.localCompare(a) // -1