The other distinction is that Chromecast pulls everything from the cloud, while AirPlay also works with media stored on your device. It's a frustrating limitation; you feel like you should be able to easily beam your own photos, videos, and music from your smartphone to the Chromecast, but that doesn't work without venturing into third-party solutions.
After you get a video playing, your smartphone or tablet acts like a remote. You can pause content or use the scrubber at the bottom to skip forward or back. You can even adjust the volume using your device's hardware volume controls, although in my testing it adjusted only the Chromecast's internal volume, rather than the volume on the TV, so you'll still need your TV's remote around for master volume control. Another perk is that any compatible device on the network can grab control of your Chromecast and can make adjustments. It's undeniably fun to have a group of friends trading YouTube videos on your TV.
Image quality from Netflix, YouTube, and Google Movies & TV was excellent -- as good as you'd expect from a more sizable streaming box. "Arrested Development" on Netflix looked as good as it does via my Roku 3, and high-quality content from YouTube like "Speakeasy with Paul F. Tompkins" also looked great. You're not making any image quality compromises by streaming with a stick.
By pushing all of the interaction to smartphones and tablets, one surprising result is that the Chromecast doesn't really have much of its own user interface. When you're not streaming, the Chromecast displays some pretty nature photos and status information, but you can't navigate to apps or select any content from your TV. In other words, there's no way to use the Chromecast as a "standalone" device -- you need to have a smartphone or tablet handy. For households where not everybody has a smartphone or mobile device, a Chromecast may not be the best choice.
Screen mirroring: Not the panacea you've hoped for
The other way to get content to the Chomecast is by using the Chrome browser on a Windows PC, Mac, or even most of Google's own Chromebook laptops. By using the Chromecast extension, you can mirror any tab in Chrome on your TV, including any video, music, or photo that works in your browser.
In my experience, screen mirroring is one of those features that sounds great (free Hulu on my TV!), but it's usually just clunky enough that you find yourself not using it that often in the real world. The Chromecast's mirroring feature is no different. It "works," but it's not a very satisfying experience.
The good news is that mirroring works with essentially any streaming video, albeit with a few seconds of lag. I tested free Hulu content, NBC, CBS, and Fox, all of which worked. The bad news is that its limitations are obvious right away. Image quality ranges from mediocre to poor, mostly because Chrome is converting the video on the fly from your PC and sending it to the Chromecast. You're also going to run into occasional (and sometimes frequent) dropouts -- sometimes just audio, but sometimes the video pauses, too. And the feature itself isn't entirely stable, so expect the extension to crash sometimes, with Google throwing a quirky "brain freeze" message up on your TV.
Performance is dependent on your home-networking equipment, wireless environment, and computer's performance, so it's possible that the Chromecast may fare better in your setup. However, I had a much better experience using the same hardware with the screen-mirroring capability built into OS X and the Apple TV, so some of the fault has to fall on the Chromecast.
Personally, I find it hard to get excited about this functionality once you've become accustomed to the excellent image quality and reliability of services like Netflix and HBO Go.
Can it compete with the Apple TV and Roku?
The Chromecast is smaller and cheaper than its competitors, but it loses out on most other counts. The Roku 3 and Apple TV have more content, more flexibility, and are just plain better suited to everyday use in your living room. But they also cost nearly three times as much, so it's not exactly a fair comparison.
The better comparison for the Chromecast is the Roku LT ($50). It supports many more services (including Amazon Instant, MLB.TV, Rdio, PBS, Watch ESPN, Vudu, and Disney Channel), has a great user interface, and can also be controlled by both Android and iOS devices. You can view photos and listen to music stored on your phone using the Roku app, plus it even handles personal media files stored on a PC using the Plex app. The Roku LT is limited to 720p output, but I've still found its image quality to be nearly identical to 1080p streamers in testing. One nagging complaint is that the Roku LT, unlike the Roku 3, still doesn't have a YouTube app, although Roku is promising it's coming soon.
Conclusion: Crucial for Android fans, and getting better for everyone else
Even though the Chromecast isn't quite as capable as competing boxes, it's still an important device for dedicated Google ecosystem fans. If you prefer to store and purchase your content through Google's infrastructure, your options for watching that content on your TV have been limited: a few buggy Google TV devices and the notoriously short-lived Nexus Q. The Chromecast finally offers a reasonable way to watch and listen to Google Music and Google Movies & TV content in the living room, without much of an additional investment.
For everyone else, the appeal mainly comes down to price. If you're fine with the Chromecast's current limitations or don't want to spend an additional $15 for the Roku LT, it's a solid option at an extraordinary price. But given that a media streamer is a product you'll likely use almost every day, most people would be better off spending a little more for a better box.