I also have a ASUS Zenbook Prime. I bought it based on Jeff Atwood's glowing recommendation on his blog. I am running Ubuntu 13.10, which fixed several hardware issues and possibly introduced a couple more. Here are my main issues with running Ubuntu:

1. Ubuntu does not remember screen brightness after reboot.

2. Getting Flash properly installed so I could watch Amazon Instant Video was a struggle. Netflix over Wine works like a charm if not ideal (it's broken for me a couple of times but it's working again now) and HBO GO works even better.

3. Firefox does not seem to support high DPI screens for Linux yet. So you either have to zoom on each page or use an add-on such as NoSquint.

4. The SSD is apparently too fast for lightdm, the logon software, to handle. I had to change the default logon software to gdm.

5. Frequently, the feature which saves Facebook/Google/Twitter login info for desktop apps would forget my password and generate blank popups and error reports.

6. Random error popups every once and a while.

All of the above are minor gripes considering I am not paying anything for this software. Overall, I am very happy with the entire stack from Ubuntu to the Linux kernel. I choose to do most of my home desktop activities on Ubuntu when possible. I keep my Windows desktop around to run iTunes and that's about it. I like the Ubuntu/Linux experience but the above problems prevent me from recommending it to my family.

Issues with ZenBook Prime:

1. Touchpad is not great.

2. I have hardware problems with the keyboard and the power and I've had to send it back to ASUS for repair. Seems to be working fine now.