As PRR60 mentioned, the two stations are indeed very different. However, even if you did somehow miss NY's Penn station, you could still make the switch at Newark's Penn station. NY however is a much nicer station to wait at.
Now just to help make sure that you don't miss it. First off, I'm sure that the conductor will make an announcement prior to arrival. Second, NY Penn comes first as you travel south, with Newark being the second.
Finally a few warning signs. About 10 minutes before you are due into NY's Penn station, you will find yourself on a very large bridge. Off to the right of the trains forward motion, you will have a wonderful view of Manhattan.
About 5 minutes later the train will go into a tunnel under the East River, before emerging into NY Penn Station. This station is huge and you will see multiple trains on many different tracks. This is the only tunnel on the run from the Boston area to NY.
Once you are upstairs in the station you can find plenty of places to eat. There is also a special waiting area for Amtrak passengers, where you can find seats to relax on while waiting for your next train.