Amtrak because of the coffee/water and café car and more spacious bathrooms, and the generally better, smoother ride. Amtrak can offer triple the legroom of most stagecoaches.
Your seat is all but guaranteed on Amtrak, though they do oversell some routes. There is no such guarantee on Greyhound, though they have made improvements on their ticketing system in the past 20 years, they still oversell and lost luggage complaints are more common on Greyhound than Amtrak.
Last but not least, Amtrak has a slightly more flexible rebooking policy than Greyhound. With Amtrak as long as you notify their customer service in time, you can apply 100% of your trip's value to a future trip whereas with greyhound some or all of this value may be lost unless you can even get to an agent before their deadline, or to get such a deadline waived, then they could rebook you, usually at an additional cost though.