The Xscope mirror, a free tool works without needing VNC but you need a paid companion app on the Mac to send the data.
I prefer to use screens on the iPad. VNC is the way that OS X sends it's video remotely to another display. If you don't use it, someone else needs to re-write that entire stack and it works very well for local networks.
As for why the app I recommend, it has an observe mode and seems to scale the screen much better than the Xscope app since it is designed primarily for designing, not mirroring. The same program works on iPad, iPod, iPhone of all sizes and retina or not displays. It is very fast and has an observe only mode so that you don't accidentally send touch events.
If you do decide to use it on the go for remote access, there is a free location app (similar to how Back to My Mac works) and works over ssh tunnels if you prefer more security than speed. It has great soft keyboard support and of course works with Linux and Windows as well. There is nothing I can say bad about it in terms of missing features os bugs or design.
It's a quality piece of software all around.
If you really must avoid VNC, there is another option. The Xscope app for software designers has a free companion app that runs on the iPad and will mirror your screen. It's more designed for counting pixels and looking at mockups you design on the Mac for eventual use on the iPad, but you can use it as a mirroring solution. It lacks any input from the iPad and simply sends the screen from the Mac to iOS.
It also is very high quality software - and is well designed, all around and fast.
Okay, after dealing with this for quite some time, I finally found a solution that worked for me. I figured I'd come and share for others as well.
In order to resolve the choppy playback, I ultimately went in to Settings -> General -> Reset -> Reset All Settings. After resetting, the device downloaded the very latest OS for the Apple TV, and after everything was done, the Airplay quality between the MacBook and AppleTV is actually pretty decent.
In testing, I was able to mirror my display without any noticeable choppiness. I was also able to extend my desktop on to the TV, and this worked surprisingly well. Even playing YouTube videos was of decent quality, with almost zero choppiness during playback.
What I have not tried yet... and will update this answer later on, is reconnecting my photo streams. As it's common to have 1000+ photos in my shared streams, I'm concerned that this may have slowed the device down (just a guess, honestly). I'll do some more testing today, mirroring as is, then adding the photo streams and comparing, to see if that causes any issue. If it does, I can always reset again.
Best Answer
This will do the trick: