When using my miles to book award travel, I personally prefer non stop over connection flights. That is, unless I plan to stop over in the one city most airlines allow you to do that at when traveling on awards.
I can see how in some cases, paying to fly may warrant desired connections in some certain combination so a mileage run can obtain more miles as a result, but when USING miles to attain award travel, why, unless there are no other choices, would someone want to stop more?
Do YOU like non stop over connection flights for your award travel?
if so why? if not, why?
One more side note: If you booked award travel and thusly planned on traveling a non stop and suddenly the airline changed this reservation on you so you now need to connect, would it bum you out? Would you wish to rebook and try to get non stop if you could? Would you spend more miles to do it?

MM