One critical note at the beginning, NEX-series cameras have interchangeable lenses, RX100 is a fixed-lens camera. Both of these are excellent choices, but I would prefer NEX-5N over the NEX-F3 from the NEX series (you get a better camera for almost same money). Both the RX100 and NEX-5N have excellent feature sets and video capabilities.
The question here is, do you value more RX100's tiny size (it fits easily in your pocket) or NEX-5N's/NEX-F3's slightly better low-light performance?
The NEXs are usually provided with a kit zoom lens (Sony SEL-1855). Using this package and comparing it to RX100's portability, the RX100 beats it 100 to 0. However, if you use the NEXs with the Sony SEL-16F28 pancake lens, you get an almost pocketable DSLR, but the lens has no zoom.
But considering your priorities, I would choose the RX100 because it will always be with you.
Some good reviews:
http://www.dpreview.com/reviews/sony-cybershot-dsc-rx100/
