D600: Eye-Fi or Wu-1B ?1

I just ordered the D600 and Wu-1B but I noticed that in the D600 brochure Nikon makes a point of mentioning Eye-Fi compatibility.

I there a reason to chose Eye-Fi over Wu- 1B? Do they offer different features?

I know nothing about wireless tethering. My biggest concern when I have shot my D700 tethered by USB cord is that the camera only writes to the computer and not to the card. In addition this disables review on the LCD.

Does wireless tethering of the D600 allow wireless transfer of images and simultaneous card recording? Can you still review images on the LCD?

Thanks for your help and advice, Jeff