The one advantage I've heard about taking the train is that prices are usually flat. If you need to book a trip the next day you will pay through the nose for most airfare. Train trips on the other hand will mostly be the same price no matter when you book. Aside from that small exception, air travel is MUCH faster/cheaper/convenient.
I have taken probably 15 Acela rounds trips in the last 3 years between Boston and NYC for work and I personally find it more convenient than flight travel.
In my case, it's easier for me to get to South Station in Boston than to get to Logan Airport. The seats and accommodations are much better on a train, much less stressful and easier boarding process (and I have precheck). I have never had an issue finding overheard space. Once in NYC, it's also easier to get to the part of Manhattan that I need to than any NYC airport. Flying is still a little faster, but my employer encourages we travel during work hours, so I don't mind the extra time for the better experience.
Obviously if I was going all the way to DC from Boston, it would't make as much sense, but since NYC is close enough, speed is basically a wash.
Next-day train tickets do increase in price, particularly on these Acela lines. However you do escape the aggressively hyperoptimized pricing for airlines, and fares become flat once you're booking about a week ahead.
