Ok, I have tested adding, iterating and removing elements from both an array and a set. I ran a "small" test, using 10 000 elements and a "big" test, using 100 000 elements. Here are the results.

Adding elements to a collection

It would seem that the .push array method is about 4 times faster than the .add set method, no matter the number of elements being added.

Iterating over and modifying elements in a collection

For this part of the test I used a for loop to iterate over the array and a for of loop to iterate over the set. Again, iterating over the array was faster. This time it would seem that it is exponentially so as it took twice as long during the "small" tests and almost four times longer during the "big" tests.

Removing elements from a collection

Now this is where it gets interesting. I used a combination of a for loop and .splice to remove some elements from the array and I used for of and .delete to remove some elements from the set. For the "small" tests, it was about three times faster to remove items from the set (2.6 ms vs 7.1 ms) but things changed drastically for the "big" test where it took 1955.1 ms to remove items from the array while it only took 83.6 ms to remove them from the set, 23 times faster.

Conclusions

At 10k elements, both tests ran comparable times (array: 16.6 ms, set: 20.7 ms) but when dealing with 100k elements, the set was the clear winner (array: 1974.8 ms, set: 83.6 ms) but only because of the removing operation. Otherwise the array was faster. I couldn't say exactly why that is.

I played around with some hybrid scenarios where an array was created and populated and then converted into a set where some elements would be removed, the set would then be reconverted into an array. Although doing this will give much better performance than removing elements in the array, the additional processing time needed to transfer to and from a set outweighs the gains of populating an array instead of a set. In the end, it is faster to only deal with a set. Still, it is an interesting idea, that if one chooses to use an array as a data collection for some big data that doesn't have duplicates, it could be advantageous performance wise, if there is ever a need to remove many elements in one operation, to convert the array to a set, perform the removal operation, and convert the set back to an array.

Array code:

var timer = function(name) {
  var start = new Date();
  return {
    stop: function() {
      var end = new Date();
      var time = end.getTime() - start.getTime();
      console.log('Timer:', name, 'finished in', time, 'ms');
    }
  }
};

var getRandom = function(min, max) {
  return Math.random() * (max - min) + min;
};

var lastNames = ['SMITH', 'JOHNSON', 'WILLIAMS', 'JONES', 'BROWN', 'DAVIS', 'MILLER', 'WILSON', 'MOORE', 'TAYLOR', 'ANDERSON', 'THOMAS'];

var genLastName = function() {
  var index = Math.round(getRandom(0, lastNames.length - 1));
  return lastNames[index];
};

var sex = ["Male", "Female"];

var genSex = function() {
  var index = Math.round(getRandom(0, sex.length - 1));
  return sex[index];
};

var Person = function() {
  this.name = genLastName();
  this.age = Math.round(getRandom(0, 100))
  this.sex = "Male"
};

var genPersons = function() {
  for (var i = 0; i < 100000; i++)
    personArray.push(new Person());
};

var changeSex = function() {
  for (var i = 0; i < personArray.length; i++) {
    personArray[i].sex = genSex();
  }
};

var deleteMale = function() {
  for (var i = 0; i < personArray.length; i++) {
    if (personArray[i].sex === "Male") {
      personArray.splice(i, 1)
      i--
    }
  }
};

var t = timer("Array");

var personArray = [];

genPersons();

changeSex();

deleteMale();

t.stop();

console.log("Done! There are " + personArray.length + " persons.")

Set code:

var timer = function(name) {
    var start = new Date();
    return {
        stop: function() {
            var end  = new Date();
            var time = end.getTime() - start.getTime();
            console.log('Timer:', name, 'finished in', time, 'ms');
        }
    }
};

var getRandom = function (min, max) {
  return Math.random() * (max - min) + min;
};

var lastNames = ['SMITH','JOHNSON','WILLIAMS','JONES','BROWN','DAVIS','MILLER','WILSON','MOORE','TAYLOR','ANDERSON','THOMAS'];

var genLastName = function() {
    var index = Math.round(getRandom(0, lastNames.length - 1));
    return lastNames[index];
};

var sex = ["Male", "Female"];

var genSex = function() {
    var index = Math.round(getRandom(0, sex.length - 1));
    return sex[index];
};

var Person = function() {
	this.name = genLastName();
	this.age = Math.round(getRandom(0,100))
	this.sex = "Male"
};

var genPersons = function() {
for (var i = 0; i < 100000; i++)
	personSet.add(new Person());
};

var changeSex = function() {
	for (var key of personSet) {
		key.sex = genSex();
	}
};

var deleteMale = function() {
	for (var key of personSet) {
		if (key.sex === "Male") {
			personSet.delete(key)
		}
	}
};

var t = timer("Set");

var personSet = new Set();

genPersons();

changeSex();

deleteMale();

t.stop();

console.log("Done! There are " + personSet.size + " persons.")

I know this is an old question, but I was double checking the data. I too assumed Set.has would be O(1) or O(log N), but in my first test, it appeared to be O(N). The specs for these functions hint as much, but are quite hard to decipher: https://tc39.es/ecma262/#sec-array.prototype.includes https://tc39.es/ecma262/#sec-set.prototype.has Elsewhere, though, they also say that Set.has must be sublinear-- and I believe modern implementations are.

Empirically, Set.has demonstrates linear performance when I ran it in some code playgrounds... but in real environments like node and chrome, they there were no surprises. I'm not sure what the playground was running on the back end, but perhaps a Set polyfill was used. So be careful!

Here's my test cases, trimmed down to remove the randomness:

const makeArray = (size) => [...Array(size)].map(() => size);

const small =  makeArray(1000000);
const medium = makeArray(10000000);
const large =  makeArray(100000000);

const solution1 = arr => {
  console.time('Array.includes');
  arr.includes(arr.length - 1)
  console.timeEnd('Array.includes');
}

const solution2 = arr => {
  const set = new Set(arr)
  console.time('Set.has');
  set.has(arr.length-1)
  console.timeEnd('Set.has');
}


console.log('** Testing small array:');
solution1(small);
solution2(small);
console.log('** Testing medium array:');
solution1(medium);
solution2(medium);
console.log('** Testing large array:');
solution1(large);
solution2(large);

In Chrome, though:

** Testing small array:
VM183:10 Array.includes: 1.371826171875 ms
VM183:17 Set.has: 0.005859375 ms
VM183:25 ** Testing medium array:
VM183:10 Array.includes: 14.32568359375 ms
VM183:17 Set.has: 0.009765625 ms
VM183:28 ** Testing large array:
VM183:10 Array.includes: 115.695068359375 ms
VM183:17 Set.has: 0.0048828125 ms

In Node 16.5:

Testing small array:
Array.includes: 1.223ms
Set.has: 0.01ms
Testing medium array:
Array.includes: 11.41ms
Set.has: 0.054ms
Testing large array:
Array.includes: 127.297ms
Set.has: 0.047ms

So, yeah, Arrays are definitionly linear, and Sets are much faster.