I have driven both pretty recently. I love the way the X3 handles, it is simply sportier to drive bottom line. If I was was racing on a track I would choose the X3. It also has more cargo room.
For real life I think the NX 200t is the choice. The seats are about the best I've experienced in terms of combining both comfort and support. The car is still fun to drive but a notch towards comfort vs the X3. The back seats are nearly as nice as the front, rare in a small SUV. This will be an easy highway trip car but still a definite step up from say a RAV4 on backroads where you can do some driving.
The clincher for me, as someone who likes quality but has a frugal side that pushes me to keep my cars for a long time, is the expected long-term reliability. If I was a serial 3 year leaser it would be a tough choice, but as a buy and hold person the Lexus is my choice.