Recently we went to visit my family in CT for a weekend. It was tricky to get tickets and we didn't want to spend a bundle, so we flew up and rode the Amtrak train back. Which is better? Well here's the TL;DR - it depends on what you value. Read more to find out!
Getting on and off is SO MUCH QUICKER! No security theater, no baggage checking and scanning, no emptying all your pockets and forgetting something and get more delays and all that garbage. It takes a couple minutes to step off the platform onto the train and find your seat.
You have so much space! You can stretch out, walk around, plug in (plenty of outlets), find the dining cart (long trains have them) and order something, and not get all cramped up. There's even WiFi, but if the train is full then it's gonna be slow and spotty.
You have a decent view - the train is relaxing and you ride through some nice areas. There's lots to see out there and it's not too hurried, just chugging along.
You can bring all your stuff. I don't know that there's any baggage restrictions, it just has to fit in the luggage bay or in overhead storage. There's under-seat space as well so you have plenty of room for stuff (including liquids and fragile things and personal electronic devices that can stay fully powered on the whole trip).
Bigger restrooms - it's still going to have some 'turbulence' as you're bouncing along, but it's nice to have a little extra space.
Getting to your destination is SO MUCH QUICKER! Even with the security stuff, still much quicker. For our usually trips, it's a generous 2.5hrs to get from our house in MD to my parent's house in CT. The train is around 6.5hrs.
You have personal service - you can (usually) get assigned seats so you sit with your people, the attendants ask what you'd like to drink and give you a snack, and you can fall asleep knowing you won't miss your stop because everyone (usually) is getting off and even if not, they check that only the correct people stay on.
Everyone boards together! You are getting on an empty plane, so as long as you get a good position or have assigned seating, then you can sit with your people! Unless you are boarding the train at the end of the line, there are already people in it and if it's a busy one (like from New Haven through NYC to DC), then you might struggle to find two open seats near each other.
They only check your ticket once! You scan your ticket, board, then can zone out (except for the safety briefing) until you reach your destination. No checking your ticket each time you enter another zone.
Signage is great! There are lots of signs telling you where to go when to be there. The electronic signs are all around telling you which terminal and gate and such. On the train platform, you have to keep paying attention and checking and asking. It's a little stressful but it's doable.
Ticket pricing - you have to check both and it depends on a load of factors which will be cheaper.
There will be stress. It's travel, you don't want to miss your connections but things are late and early and you have to keep on your toes and leave buffers all around.
There are pros and cons to each and it depends on the time of year and what you value, but it's nice to have both options.