It can go either way. Personally I think 33" is the biggest a D44 is comfortable with (adding a few minor upgrades, blazer axles).
The brakes on a 44 start getting taxed pretty hard above 33s, that is where I really like the big brakes on a 60.
As for stock, the initial bolt in of a 44 is stock, but all the upgrades are aftermarket. And that gets into the service items as well. Where a 60 will take more work to install, but you can run many more off the shelf service items. The bigger wheel bearings on a 60 will take the loads of taller tires and there is no big bearing upgrade for a 44.
As you can tell, there is no clear way to go. I started off with a 30, shaved the teeth off the ring gear and blew out a king pin. Got a deal on a 44, disk braked it, popped an axle, did a little upgrade, popped another axle, did the high dollar shaft upgrade (but not RCV super high dollar), had to do some steering upgrades. All this on just 33s. One of the things that kept me from going to larger tires was I kept running into the limitations of the 44 on only 33s. The 9" had good guts, but was welding cracks in the stock housing, that was going to be another upgrade needed if I went bigger in the tires.