I just got back from a rather long trip through the Northeast using both Amtrak and Megabus, so I got to compare them both. In general, Megabus is quite competitive with Amtrak as far as schedule and pricing goes. I rode Megabus from NYC to Boston for $30 each way, while a Northeast Regional would've been at least $100 OW, booking the same distance out (the Acela was well into "if you have to ask..." territory...).
Buses on major routes in the NEC depart every hour or so, about the same as Amtrak. We were also more-or-less on time for arriving each way, despite heavy traffic in and around Manhattan, which was nice...I've heard some horror stories about other Megabus rides that were 2+ hours late, though, so take that with a grain of salt. Additionally, Megabus frequently overbooks, so make sure to get to the stop early or else you may have to wait another hour (or more) for the next bus.
I have yet to ride Megabus outside the NEC, but it looks like their schedules--at least in my area--are MUCH better than Amtrak in most cases. For example, the Megabus from Pittsburgh to Cleveland departs at 7:00AM and arrives at 9:30AM...the Capitol Limited for the same route departs at 11:59PM and arrives at 2:53AM. Easy choice to make there, regardless of the fare.
Amtrak's main advantages seem to be, as always, comfort and flexibility. Amtrak coach class seats have lots of legroom and a comfortable footrest...Megabus is more comparable to coach seating on an airline. Not UNcomfortable, and still much better than Greyhound, but not a whole lot of space to stretch one's legs. Passengers can also get up and move around the train, or switch seats if other pax are being disruptive (as happened when I rode the NE Regional from NYC-WAS)...on Megabus, you'd better hope your fellow pax are well-behaved, because there isn't much room to move around. Also, needless to say, there is no lounge or dining car on Megabus, though the driver will make rest stops along the way on longer routes. There is free wifi on both services, and I found both to be equally slow and spotty.
Then there are the departure and arrival points. Larger Amtrak stations will, of course, have a fairly spacious climate-controlled area, and even the smaller stops usually have at least a shelter. Megabus doesn't have stations...they pick you up at curbside only to cut costs...so if it's raining or snowing, too bad. (Although they do use South Station Bus Terminal in Boston.)
Also, Megabus doesn't do guaranteed connections...if you book two separate tickets and your first bus is late, missing the second, you're SOL. Amtrak will also usually issue fully refundable tickets...Megabus is "use-them-or-lose-them."
Basically, it all boils down to the best schedule for your needs and how much you value personal comfort and safety. As always, you make your choices and take your chances...