New York City Traveller Article:

New York City: Attraction Passes - An Analysis

Tripadvisor

New York is filled with bargains, deals, and steals, especially in the attraction department. There are a number of attraction passes to choose from which could save you money on attractions in New York City. Be sure to read the information carefully to determine which sights you're most likely to be seeing to choose the pass that's right for you.
KEEP IN MIND:
1. Many of the museums included, have pay-what-you-wish admission or may have "free" days.

Museum of Modern Art - Admission is free for all visitors during UNIQLO Free Friday Nights, every Friday 4:00–8:00 p.m.
For the American Museum of Natural History there is a voluntary suggested $19 donation.
Metropolitan Museum of Art operates a $25 recommended fee. You can pay the full suggested donation, but it is not mandatory. You can, in fact, pay what you wish, as long as you pay something more than one penny. These are things to keep in mind when reviewing the attractions included with each Pass.

2. The 9/11 Museum has been added to the New York CityPass as one of the alternatives - you can visit the 9/11 Museum OR the Intrepid Sea, Air and Space Museum. The 9/11 Museum is also available on the New York Pass, but it is not available on any of the Go City Card products - don't be confused with 9/11 Tribute Center, which is a different attraction but is still included in the NYP. An extra fee is payable for a guided tour of the Tribute Centre but a self guided tour is available included.
3. Visiting the Statue of Liberty and Ellis Island: note that the Passes only allow a visit to the RESERVE at the Statue, although the CityPass and the New York Pass do have some PEDESTAL tickets available on a daily, first come first served basis at extra cost. This upgrade option is NOT available on ANY of the other passes. You cannot upgrade to the Crown on any pass. It is adviseable to pre book online for pedestal tickets and crown tickets. Crown tickets often sell out months in advance and limited numbers are available.
4. The City Pass does included the Statue of Liberty. Yes, it's only the Reserve, BUT there are some Pedestal tickets available to holders of City Passes and New York Passes each day on a first come first served basis.
There are 3 companies in New York City that offer Attraction Passes (below in alphabetical order)

City Pass Tear out coupons for 6 New York Attractions comprising:
1) Empire State Building Observatory;
2) The Metropolitan Museum of Art (a suggested-donation-admission museum) and the Cloisters (if you visit BOTH within a week);
3) American Museum of Natural History (a suggested-donation-admission museum) & Rose Center;
4) Guggenheim Museum OR Top of the Rock;
5) Statue of Libery and Ellis Island OR Circle Line Sightseeing Cruises and
6) 9/11 Memorial (free) and 9/11 Museum OR Intrepid Sea, Air and Space Museum.
Good for 9 days.
Prices: $116 for adults, $92 for youths (6 – 17).
Best for: Travelers who want to see at least 4 of the named attractions. Great for someone in town for one week although do remember The Met and AMNH both operate a suggested* price policy. The best part of this pass is that you have nine days to use it, and can visit all the attractions at a comfortable pace, though this Pass is limited to only 6 attractions (some with alternatives).
New - there is a 3 attraction option CityPass available that can save up to 25% of entry. Simply choose any 3 out of the CityPass attractions, that Pass costs $71 for Adults and $51 for Children.
*Visitors can pay any amount with which they are comfortable (from 1¢ up). You must go to the sight to purchase these tickets - they are not available online.

New York Pass - offers entry to over 80 Attractions in NYC and it is the only Pass that has no limit to how many attractions can be visited by Pass holder.

Passes are available for 1, 2, 3, 5, 7 & 10 days, valid for consecutive use
All Passes include Big Bus Hop-on Hop-off bus tours - unlimited use for 24 hours (1 day pass) or 48 hours (2,3,5,7 & 10 day pass)
It offers admission to many iconic attractions such as Empire State Building, Ferry to Statue of Liberty, 911 Museum & Memorial, Madamme Tussaud, Full Manhattan Island Cruise, Top of Rockefeller Center, Radio City Music Hall, Carnegie Hall
Rich in themed tours: Food tours, Central Park by bicycle, Gospel, Brooklyn Bridge, Wall Street. High Line Park, Greenwich Village, Yankee Stadium, Madison Square Garden and more
15 Attractions offer Fast Track Entry,
17 attractions can be reserved in advance
200+ page guidebook and App (iOS and Android) are available online for free

Prices: from $109 for 1day to $349 for 10days: Child option (4-12) available. Buy online for better prices
Savings: Possible savings can be really big, seeing 3 attractions a day can save over 70% on entry fees, with longer duration Passes that can be over $200 - $500 per person.
Best for: Travelers who want to see & do it all, active travelers who like convenience and visit 2+ attractions per day. Good for people who like to plan their trip in advance and first time visitors that would like to see most of NYC. Big savings if you see a lot
Drawback: Of course the price itself seems like a lot of money all at once, so those on tight budgets might be ruled out altogether. Another thing to seriously consider before buying a New York Pass is that doing even 3 or 4 main sights in a day is going to be busy and probably frantic.

The Go City Card company offers 3 different products that save travelers money on combined admission to top New York City attractions:
Build Your Own Pass

How it works: Choose 2 or more attractions you want to visit from over 65 options, add them to the pass, and save 15%-25% on combined admission. With instant delivery, you can print your Pass at home or use it right on your mobile device. Passes are valid for 30 days from activation at first attraction visit.
Attraction choices include: Empire State Building, Top of the Rock, American Museum of Natural History, Metropolitan Museum of Art, The Museum of Modern Art, Statue of Liberty & Ellis Island Ferry Ticket, Downtown Manhattan Hop-On Hop-Off Bus Tour, and many more.
Savings example: If you bundle the Empire State Building, the Museum of Modern Art, and Intrepid Museum: Space Shuttle, the cost of the pass is $64.80 saving 20% vs. paying for each attraction at the gate.

Best for: People who know which attractions they want to see, on-the-go travelers who can buy the pass last minute and use it right on their smartphone.
Drawback: Those who’ll be staying in New York City for over a week and would prefer to see sights at a slow pace
New York City Explorer Pass®

How it works: This multi-attraction pass that includes admission to your choice of 3,4, 5, 7, or 10 New York City attractions, depending on which pass you purchase, for one price. Choose from over 55 top attractions for a savings of up to 45% vs. paying at the gate. You can get a physical card in the mail, print your Pass at home, or use it right on your mobile device (recommended). Passes are valid for 30 days from activation at first attraction visit.
Attraction choices include: Top of the Rock, Empire State Building, CitySights Bus Tours of New York City, Statue of Liberty & Ellis Island Ferry Ticket, American Museum of Natural History, The Museum of Modern Art, 9/11 Tribute Center & Tour, and many more.
Savings example: Use the 3-Choice New York City Explorer Pass ($76/ adult) at Central Park Sightseeing: Full Day Bike Rental, Circle Line Sightseeing: Semi-Circle Cruise, and CitySights: Downtown Manhattan Hop-On Hop-On Tour and save 50% vs. paying for each attraction separately.
Prices: range from $77 (3 attractions) to $180 (10 attractions) based on the number of attractions chosen. Child passes (ages 3-12) available.

Best for: Travelers who want flexibility as you don't have to commit to attractions in advance. Easy to sample the attractions in the city without feeling overwhelmed, but limited to maximum 10 attractions. Great option if you want to keep your itinerary flexible in the event of weather or sudden changes in your itinerary.
Package Deals

How it works: Multi-attraction passes that include admission to pre-determined attractions for one low price for a savings of up to 30%, depending on which pass you purchase.
Pass choices include: Top 4 Attraction Pass, Spectacular City Views, New York City Museum Pass, New York City Sightseeing Pass, and NYC Land & Sea.
Savings example: The Top 4 Attraction Pass includes admission to Hop-On Hop-Off Downtown Tour by CitySights, Empire State Building, Lady Liberty Cruise, and 9/11 Tribute Center and Tour for $89 and a 32% savings vs. paying for each attraction at the gate.

Best for: People looking for itineraries tailored to their specific sightseeing interests, people who know which attractions they want to see, on-the-go travelers who can buy the pass last minute and use it right on their smartphone.

Summary
It’s best to do your research first, see what attractions you want to visit and then decide if and which Pass fits your needs. Your savings will depend on what type of visitor you are. Having a Pass in NYC is a convenient way to see the city, so if money is not the only deciding factor, then you should enjoy those. Should you decide to get a Pass, get it online - usually you will get a better price. Plan ahead - enjoy NYC
1. CityPass
2. New York Explorer Pass
3. New York Pass