No, it is definitely not as easy. Aside from the 3 train rides and hauling baggage around on trains that others have mentioned, if you book by air, your bags will be checked through all the way to AMS from PHL. You will not need to do anything at JFK other than walk from your arrival gate to your departure gate. If it's the same airline or a partner operating from the same terminal, you won't need to go through security again at JFK.
If you fly, you will only need to touch your bags and clear security at PHL, so you won't need to plan a long layover at JFK if it's all booked on one ticket. On the other hand, if you take the train, you'll need to plan more time at JFK, as you'll need to wait in line to check your bags and wait in line to clear security. Depending on terminal, airline, time of day, whether you have TSA PreCheck, your status with the airline(s) in question, and your booked class of service, this could take anything from a few minutes to more than an hour. It will definitely take more time than just walking from your arrival gate to your departure gate if it's booked on the same airline.
Note, however, that the above only applies to the direction you've indicated: PHL-JFK-AMS. For the reverse route, the same would not be true. For AMS-JFK-PHL, you would need to clear U.S. immigration and customs at JFK and then clear security again in order to get to your connecting flight to PHL. When arriving in the U.S., you always have to either clear U.S. immigration at your first port of arrival (the normal case) or at the last airport before arriving in the U.S. (in the case of airports that have U.S. immigration preclearance, which AMS does not.)
Also, as other answer have mentioned, if you book on a single ticket, the airline will be responsible for ultimately getting you to AMS in the event of a missed connection. On the other hand, if you book rail and air separately, you will potentially be on the hook for the consequences of a missed connection if the trains are delayed.