To the best of my knowledge, the Prime (UA21A) only uses the Intel HD 4000 integrated graphic core. The UX32VD comes equipped with a nVidia GT 620m. Other major difference is the size of the laptop; the Prime has a 11.6" screen and the UX32VD has a 13.3" screen. The larger screen makes things easier to read, but also increases the weight and increases power consumption which reduces battery life. Lastly, the Prime can only be equipped with up to a 256GB SSD while the UX32VD comes with a 500GB hard drive with 24GB SSD cache.
Obviously, the UX32VD will provide better gaming results because of the GT 620m, but it is a somewhat weak card. I have seen some game benchmarks where the Intel can actually beat it's little brother the GT 610m. In fact, based on those results the Intel HD 4000 is actually better than the GT 610m. The GT620m is faster than the Intel HD 4000 and the GT 610m, but not by very much