I'll answer my own question and hopefully this will save someone a little research in the future. I picked up a used, rooted Galaxy Note 10.1 running Jellybean last night. I'm not going to delve into the software comparisons yet because I've only played with the Note for a few hours. But I'd like to give my first impressions.
The Asus, with the aluminum backing just feels so much more solid than the plastic Note. I've read/heard in the past that Asus has some quality-control issues, but my TF201 feels rock solid and I haven't had any problems with build. As well, the Asus feels noticeably thinner in the hands (when it's only fractionally thinner by design). So I would give the Asus better marks for initial feel of the device.
But, the overall design of the Note 10.1 is more appealing. The front facing speakers of the Note blow the Asus out of the water. The speakers add some charm to the face of Note instead of the plain black bezel of the TF201. And the screen on the Note is brighter, more vibrant, and text looks much better. So I would give the Note a higher score in overall design.
As far as the software goes, the installed Rom on the Note was a little glitchy, so it's not a fair comparison. The Note runs 4.0.4 out of the box, but Jellybean is coming soon. The Asus, on the other hand, is running Jellybean direct from Asus and I've had no problems whatsoever. But since both were on JB, I'll give you my first impressions.
I really didn't notice either tablet beating the other in my everyday use tests, ie Maps, Browsing, Swiping, Opening/Closing Apps, etc. The one thing that was annoying was that I couldn't load Adobe Flash onto the Note, but I have it on the TF201. I know this is because JB isn't compatible and Adobe has stopped supporting it, but I couldn't even sideload it. Strange. I didn't spend enough time on it, so don't take this as 100%, but it could be a problem for someone that must have Flash.
But other than the Flash player issues, neither tablet noticeably beat out the other. It's a really pleasant experience on either tablet and I don't think you'd be disappointed owning either.
This is just a first impressions summary, so take this with a grain of salt. Good luck to all!