I spent a little time googling and reading.
From what I found, it looks like the JK Sport has 9.7" of clearance and the Rubicon 10.8", despite the D44 having a larger pumpkin.
The Rubicon has stiffer springs, but they are dimensionally (uncompressed) the same as the other models. This results in less body weight spring compression and a slightly higher stance. Most sources I found say it's an inch or so. The rest of the added clearance is from the larger OEM tire. There are also reports that some non-Rubicon models were sold with Rubicon springs. So it seems like time to grab your tape measure.
The general consensus seems to be that you can fit 33" tires on non-Rubicon models and 35" on Rubicons without a lift. Both are often (but not always) reported to rub when flexed. Clearly there is a fair bit of variance between vehicles.