How can I check that two objects have the same set of property names?

You can serialize simple data to check for equality:

data1 = {firstName: 'John', lastName: 'Smith'};
data2 = {firstName: 'Jane', lastName: 'Smith'};
JSON.stringify(data1) === JSON.stringify(data2)

This will give you something like

'{firstName:"John",lastName:"Smith"}' === '{firstName:"Jane",lastName:"Smith"}'

As a function...

function compare(a, b) {
  return JSON.stringify(a) === JSON.stringify(b);
}
compare(data1, data2);

EDIT

If you're using chai like you say, check out http://chaijs.com/api/bdd/#equal-section

EDIT 2

If you just want to check keys...

function compareKeys(a, b) {
  var aKeys = Object.keys(a).sort();
  var bKeys = Object.keys(b).sort();
  return JSON.stringify(aKeys) === JSON.stringify(bKeys);
}

should do it.

2 Here a short ES6 variadic version:

function objectsHaveSameKeys(...objects) {
   const allKeys = objects.reduce((keys, object) => keys.concat(Object.keys(object)), []);
   const union = new Set(allKeys);
   return objects.every(object => union.size === Object.keys(object).length);
}

A little performance test (MacBook Pro - 2,8 GHz Intel Core i7, Node 5.5.0):

var x = {};
var y = {};

for (var i = 0; i < 5000000; ++i) {
    x[i] = i;
    y[i] = i;
}

Results:

objectsHaveSameKeys(x, y) // took  4996 milliseconds
compareKeys(x, y)               // took 14880 milliseconds
hasSameProps(x,y)               // after 10 minutes I stopped execution

If you want to check if both objects have the same properties name, you can do this:

function hasSameProps( obj1, obj2 ) {
  return Object.keys( obj1 ).every( function( prop ) {
    return obj2.hasOwnProperty( prop );
  });
}

var obj1 = { prop1: 'hello', prop2: 'world', prop3: [1,2,3,4,5] },
    obj2 = { prop1: 'hello', prop2: 'world', prop3: [1,2,3,4,5] };

console.log(hasSameProps(obj1, obj2));

In this way you are sure to check only iterable and accessible properties of both the objects.

EDIT - 2013.04.26:

The previous function can be rewritten in the following way:

function hasSameProps( obj1, obj2 ) {
    var obj1Props = Object.keys( obj1 ),
        obj2Props = Object.keys( obj2 );

    if ( obj1Props.length == obj2Props.length ) {
        return obj1Props.every( function( prop ) {
          return obj2Props.indexOf( prop ) >= 0;
        });
    }

    return false;
}

In this way we check that both the objects have the same number of properties (otherwise the objects haven't the same properties, and we must return a logical false) then, if the number matches, we go to check if they have the same properties.

Bonus

A possible enhancement could be to introduce also a type checking to enforce the match on every property.

If you want deep validation like @speculees, here's an answer using deep-keys (disclosure: I'm sort of a maintainer of this small package)

// obj1 should have all of obj2's properties
var deepKeys = require('deep-keys');
var _ = require('underscore');
assert(0 === _.difference(deepKeys(obj2), deepKeys(obj1)).length);

// obj1 should have exactly obj2's properties
var deepKeys = require('deep-keys');
var _ = require('lodash');
assert(0 === _.xor(deepKeys(obj2), deepKeys(obj1)).length);

or with chai:

var expect = require('chai').expect;
var deepKeys = require('deep-keys');
// obj1 should have all of obj2's properties
expect(deepKeys(obj1)).to.include.members(deepKeys(obj2));
// obj1 should have exactly obj2's properties
expect(deepKeys(obj1)).to.have.members(deepKeys(obj2));