Train vs. Airport
I'm going to say that the answer depends on circumstances...
In October, I had the pleasure of being stuck at the airport in Atlanta for 12 hours due to a complete meltdown of the air network between ATL and Florida. I've also been stuck on a train for 12 hours on a Texas Eagle journey about 14 years ago when UP (I think?) was in the process of double-tracking part of the route.
Everyone was hoping to get out on standby, but by the time of the last flight, it was clear no one was going anywhere. Due to the size of the meltdown and late hour, there were no hotels available anywhere near the airport, and securing transportation to a remote hotel was impossible at midnight. All of the lounges were closed, so that meant sleeping in the terminal. We were fortunate to grab a couple benches that had no arm rests so we could sleep in shifts. Others had to sleep on the floor or while sitting up. During this, we learned that the lights and TV advertisements never stop, and we had to move a couple times to accommodate the cleaning crews. The next morning, we were in the 20s on standby for a flight along with 150 other people...for a 140 person flight. We gave up on flying, so we hustled to the car rental counter. National, Thrifty, and several others had no cars, but Hertz had about 10 left, so we grabbed one and drove the remaining 6 hours.
In contrast, in my 12 hour delayed Texas Eagle, I had a sleeper and didn't really notice the delay. For folks in coach, members of the crew secured a personal video device and had movie times for kids and even did story time reading. We we arrived at our destination, we hopped on a bus and ate some donuts and coffee provided by Amtrak, and caught up to our connecting train in a couple hours.
Somewhat ironically, the door to door time from Boston to our destination was about 30 minutes longer than the train schedule. On the plus side, I'll have a far easier time convincing the family to take the train next time.
Train vs. Plane
I've also had the distinct pleasure of being stuck on a train for 3 hours and on a plane for 3 hours on the same day on another Boston to Florida trip. This was the same day that Captain Sully landed in the Hudson. My Acela from Boston was constantly stopping due to freezing in the (air lines?). This included about 2 hours just before entering the tunnel to NYP. It was obvious I'd miss my connection and since this was a long weekend, I didn't want to overnight in NY, so I booked an afternoon flight from La Guardia. I made it to my flight just as boarding started. We pushed back on time, only to sit on the taxiway near the runway due to an engine issue. It took 3 hours to get the plane towed back to an empty terminal. (Meanwhile, cell phone's were buzzing and ringing as news of a plane landing in the Hudson spread). As it was a full flight and we had no engine power, there was no inflight entertainment and climate control was very lacking, so everyone was wearing full winter coats while stuffed into seats which made things very tight. å
In both cases above, being stuck on the train was far more pleasant, but as other posters have shown, "better" really depends on the circumstances.