So I baked both pies tonight. First off, I screwed up. I was trying out a new oven set up which did not go according to plan so the 2 pies were baked slightly different.
As a result of this I got a different amount of rise out of each crust. This pretty much botches the results BUT I'm confident that had all things been equal, I would have gotten the same amount of rise. I concluded this b/c both had the same relative amount of rise over the 4 days and during the proof. Both felt the same as far as being easy to open up and both had similar characteristics of extensibility, moistness, and stickiness.
Pic #1 is the ADY pie (white pie for the wife)
Pic #2 is the Natural Starter pie. (My FIRST nearlypolitan pie!

Pic #3 are the 2 crusts side by side.
Both had very similar crust and crumb structure & texture. I (who is not a SD bread fan) could not tell the difference between the 2. With multiple taste tests of the crust, both had a nice flavor and both tasted slightly sour to me.
My wife, who is the SD bread fan, said that #2 (Natural Starter crust) had a definite more sour taste to it, but that she preferred #1 crust for texture and taste. This could be due to the fact that it was baked slightly different, I don't know. I did not tell her which one was which, but just asked her if she noticed any difference in the 2.
So the results are inconclusive. It may be that my natural starter culture is a weak culture, I don't know. It could be the way I'm maintaining it and/or how often I feed it or don't as Bill mentioned previously. But my feeling at this point is that my Starter gives no more or less flavor or rise compared to ADY.
I will be receiving a different SD culture from another member soon that is suppose to be very old. I hope to revive it and run another batch of test between the 2 starters.