In practice, I have found that all hotels will fight you on this - almost every time. MR, HH, and SPG - I'm Gold in all three, and have the same experience with all three. If you want a 2PM check-out, ask for 4PM and you will probably be able to haggle down to 2PM. Don't make the 2PM request your opening gambit or else you'll get stuck with 1PM. The whole process of getting a late check-out always feels like buying a used car (including the "I need to talk with my manager" part), even on days where the hotel is obviously not sold out the following night.

Don't mean to burst anyone's bubble...I think Marriott has a fine rewards program...but I wouldn't make a switching decision between any of the big three programs based on late checkouts. It's simply too random and very subject to your own ability to negotiate with the particular staff on that day.