I don’t own either type but have been interested in building one, the other, or both, for historical demonstrations. Everything I have come across on them indicates that spring pole lathes are very simple to construct. So much so that bodgers would pack the basic tools into the deep woods, make the lathe at the camp, and then abandon it in place when it was time to move on. They appear to work better for green wood turning if that matters. The disadvantage was that you had to contend with a reciprocal motion instead of a continuous rotation when using the tool. The continuous rotation of a treadle lathe, with a heavy flywheel, gives higher speed and torque to the rotation, and allows for constant cutting action. The treadle lathe requires more investment in the construction process and normally is a heavier piece of equipment. That can make the spring pole more attractive if you are having to move it frequently and aren’t concerned with maximum production.
Another option would be a great wheel lathe and you could involve the whole family in your turning hobby. Surely your wife, kids, grandkids, neighbors, etc. wouldn’t mind spending hours on end providing power so you could turn.
Seriously, as simple as a spring pole lathe can be, why not make one and try it out. There is a lot of good information available on both types and don’t overlook the Roy Underhill (the Woodwright’s Shop) books and videos that deal with the subject. The treadle lathe has more appeal to me personally since I am used to working on an electric powered lathe.
Be sure and post pictures and/or videos and let us all enjoy your project. Have fun.