According to their schedules, Megabus is actually faster and more convenient .. and cheaper, depending on how early you book.
Looking at Amtrak, it would take 7 hours for a trip from Cleveland to Chicago, leaving only at 2:47 am or 3:45 am, costing $49 (if the trip took place tomorrow). Megabus takes 5.5 hours, leaves at 9:15 am, 5:30 pm and 11:59 pm, costing $42.