Actually "quite well" is an understatement. It plays videos impressively. The system menus are laggy because there's no X and thus no 2d accelerated desktop components, because technically there is no desktop. Distros like raspbmc and openelec don't use X. It's not even installed. Hence it doesn't consume RAM nor require configuration.
If you want a full desktop you can get the distro recommended by the raspberrypi.org that implements a desktop and allows you to run GUI apps. Even without a desktop you can still ssh into your Pi and do updates, monitor temperature, update the packages (and install new or remove old ones) from your desktop/laptop computer without having to get up and to type away at the Pi's keyboard.
If you overclock the system this performance improves. It doesn't void the warranty if you don't exceed their OC limits. Even so, it's only $35.00, so if you blow one buy another. My Pi is overclocked in all categories, which isn't hard to do nor hard to determine issues with overclocking. Adjust up or down as you see it is stable or unstable. If it helps to run this off a USB HDD rather than a flash drive (which are known to be slow to write) then do so. For simplicity sake I don't run from an external USB HDD. I do have my Drobobox attached with 4 drives installed in it, and I have samba set up so any computer can access those files from shares created on the Pi. I've played 3 videos on different computers, via these shares, including one of them on the Pi (and music on another computer) at the same time with little to no lag on the Pi.
You can also use XBMC remotes such as yatse (which is far better than the remote from the XBMC devs). You'll not notice the screen lag and it won't annoy you because you aren't interacting with the screen. XBMC can be configured to enable the web server allowing access your Pi's XBMC via your web browser (to start and stop and queue up content). With remote control software (for Android) like yatse and the XBMC dev's remote you can even browse the web (or, if you have a favorite podcast player, browse your available podcasts (either stored locally or directly from the web)), and then tell your android device to play on an external player. Doing so directs the URL to your Pi's XBMC. In otherwords you could be watching a video podcast on your Android device and with a tap tell it to begin playing that same podcast on your Pi's XBMC.
The Pi also has a distribution that is targeted to run Asterisk. Currently I have a mini itx mobo running an asterisk server. For me, it would be nice to have asterisk installed and configured with my current Pi.
There are few if any media boxes that provide DVD support. The ATV, many Google TV boxes, the ROKU, the WD media box, the Boxee Box, and the various other dual core and quad core Pi copycats don't have DVD support. Nearly no tablet (Android, iOS, nor Win8) support DVD drives yet play media well. With the Pi you can at least plug in an external DVD drive and with the right software, such as libdvdcss2, you can play back DVD content, that is, if the distro you chose hasn't removed support (which would be very short sighted). Support for any given device that is supported in Linux is also supported on EVERY Pi, IF, the distro chose to LEAVE those features in rather than remove them in an effort to shave off some memory demands. Even so, this doesn't preclude someone else from adding it back, BECAUSE Linux is Open Source, hence so are the distributions for the Pi.
There's really no comparing the ATV product to the Pi.