Upvote:4
No matter what you do, you will enter the Schengen area in Frankfurt. Flights to Amsterdam and other destinations in the Schengen area depart from another set of gates than flights out of the Schengen area and you will have to go through a passport check and get an entry stamp to reach them.
By contrast, when you land in Amsterdam, there won't be any passport check as you are already in the Schengen area.
So you might as well leave the transit area of the airport in Frankfurt if you wish. You will need a boarding pass to be able to get back in and should allow some time to clear security before catching your flight to Amsterdam.