As was said, it's probably best to check for yourself, since only you know what dates work, how important comfort and scenery is, if you have any travel restrictions, etc. Greyhound is definitely going to be less comfortable than Amtrak, and since it's apparently more expensive, I just don't see any reason you would want to take the bus.
I honestly only choose Amtrak over the airlines for long distance travel if I can take a sleeper. Flying is definitely a worse experience than coach on Amtrak, but the fact that it takes a tenth as long makes it the better option for me. I take it you are not looking into a sleeper, so I would actually recommend flying, considering it is definitely by far the fastest option, and may actually be cheapest.
All of that said, I really am speculating here, since I don't know what your budget is, if you can or can't fly, and what your dates or travel are. So could you fill us in on some of that?