Flying within Europe as an American Citizen

We flew Rome to Athens--- process like flying Seattle to Dallas

Nothing I noticed was different when flying Paris to Florence and back last summer. In Florence I showed up more than 2 hours early and had to wait til about an hour before the flight to check in.

No problem I do it all the time and American musicians I know on one night in a city concert tour do it all the time. It is like a domestic flight in the USA

As long as you stay in the Schengen zone there is no immigration or customs to deal with. Just like flying state to state in the US. Same degree of hassle -- security check, 3in1 bags, luggage screening, pat downs if you trigger the bell.

Wondering where you are going that it needs 8 hours on a train? Amsterdam to Frankfurt is less than 4 hours. Flying will take more time than that with getting there early, and the fact that many airports are not in the city center. Frankfurt is probably the closest, but you still need to figure in that time. Are you using the Deutsche Bahn website?
I prefer riding a train any day over flying. Easier, and a lot more comfortable.

Where are you actually going? Assuming it is somewhere between Stuttgart and Frankfurt it will most likely not take 8 hours by train, unless you are going somewhere really far away where you need to take a slow regional train. Amsterdam to Stuttgart takes 5:30 by train, and that is from city centre to city centre. You also don't mention when you are travelling, but showing up 2 hours before your flight at Schiphol might be on the optimistic side if it is a summer trip.

Within Schengen, an American is just part of the heard. I will fly before I sit on a train for 5 or 6 hours, so I've done it a lot. Going out of Schengen, again, you are just part of the heard (but you have to present your passport). Coming into Schengen, you are part of a diverted heard to a different window, sometimes faster, sometimes slower than the EU passport window. Really never a consideration. Same issues, or lack there of, if you take the train. Moooooooooooo

If the total transit time (getting to the station/airport, waiting time, transit time and getting to your hotel) is the same, I like the train or bus over planes. They start in town and end in town making moves easier. In both cases buying tickets early tends to save money. Hope you travel light like RS promotes. Long moves are definitely a plane ride. There are very strict luggage sizes and weights or extra fees/time to handle your luggage.

@Ms Joe I was looking at taking the train down to Baden-Baden (I need some pottery from Soufflenheim lol) . I didn't check the train going into Frankfurt. But that is good to know that it is only 4 hours from Amsterdam. We need to get a car at some point (the reason for this trip is a family reunion where having a car will be important) So taking the train to Frankfurt and picking up the car there makes a lot of sense!

Thank you!!

If your destination is Baden-Baden, it makes even more sense to take the train to Baden-Baden. Takes 5:45 from Amsterdam, plus a 10 minute bus ride from the station to the town centre. And if you want a car, you can rent it in Baden-Baden.