3 week Europe trip

I vote for option 2, but that’s because of a bias I have for one of the stops. September is a beautiful time of the year for Central Europe, so that helps too.

Option 3, since you asked. Since Paris, Rome and Salzburg show up on both of your lists I am going to suppose those are higher priorities.
Fly to Rome (4 nights)
Train to Naples (3 nights). Only showed up on one of your lists, but it a great change from typical Italy
Fly to Budapest (5 nights) on Ryan or Wizz (non-stop in 1:40, can be under $100 depending on how you pack)
Train to Salzburg (2 nights) (there is a direct train)
Fly to Paris (4 nights) (non-stop in 90 minutes on Lufthansa or Air France for about $100 if you don’t overpack) or a 7-hour train. Not sure if there is a night train; maybe
That leaves 3 unaccounted for nights. You choose which of the above to put them in. I just put what I thought were rational minimums).

Option 4. The Eastern Bloc meet West
Fly to Either Bucharest or Budva (Podgorica) or Sarajevo (5 nights with a side trips)
Fly to Budapest. From Sarajevo you will have to change in Belgrade and if you do that lay over for a night or two (very interesting city), the others all have non-stops. (4 nights)
Train to Eger / Pannonhalma (1 night)
Train to Vienna (3 nights)
Train to Salzburg (2 nights)
Shuttle to Cesky Krumlov (1 night)
Shuttle to Prague (3 nights)
Again a few nights are left over for you to pick where to use them.

Thanks for the input. Regarding why a few locations are in both itineraries is partly logistics. I am coming from Utah and there are non-stop flights from CDG home. This makes a good ending point and Paris has a lot to offer. Rome was an interesting city I would like to spend a little more time in and would be convenient to go to Naples. Naples was added as a base to spend a day visiting Pompei and a day on the Amalfi Coast. Salzburg was added as I would like to spend a couple days in Austria and Salzburg has direct trains from the other locations. Would likely do day tours from Salzburg to explore. I do not drink so doing tours up into Germany for Oktoberfest isn’t a priority.

I assume this is for next year. If it's later this month, where you can get a room should dictate where you go.
I think Option 2 makes more sense, as you'll be moving north to south, more or less following the weather. My suggestion would be to fly into and out of Paris on a regular RT ticket and begin the trip there, then train to Zurich, etc. That way, you only need the one internal flight from Naples back to Paris. Assuming an overnight flight, you could probably head to Zurich by train on your arrival day. I think the journey is about 4 hours and quite scenic. The jet lag people will tell you not to get on a train on arrival because you need to be out in the light and moving.
Be sure to take a look at Mr. E's links on Budapest. I got started down that rabbit hole yesterday, and it looks awesome.

LOL .............................................