I like the wider viewing angles on the Zenbook Prime and can live with 72 percent color gamut vs. 96 percent on the Sony Vaio Z. But either way, you're looking at top notch displays.
For what you're doing, you don't need all the power of the Z, and the UX31A could handle things just fine.
The Sony Vaio Z trackpad is tiny, though it works well. I did find my finger wandering off because it's so small. The UX31A's trackpad is larger but I like the Sony's responsiveness better. However: uninstalled Asus Virtual Touch software and the trackpad works much, much better!
I'd give the edge to the Sony keyboard, but the Asus is quite good too.
No extended battery for the Asus, as you noted. The Sony Vaio Z with sheet battery will run 2x longer than the Zenbook Prime.
-------------------- Lisa Gade Editor in Chief, MobileTechReview