Apple TV can sling more apps from mobile devices to the TV, but Chromecast's limited number of apps do it better by freeing up the device for other tasks.
Mirroring entire devices
When it comes to mirroring whole content, Apple TV and Chromecast are just as different.
In the case of Apple TV, if an mobile app doesn't support Airplay's one-button slinging approach, there's always Airplay mirroring. This option, now conveniently located in iOS 7 Control Center, broadcasts the entire screen of an iOS device to the TV.
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Airplay Mirroring also works on newer Macs running OS X 10.8 Mountain Lion; anything and everything from a Mac computer can be streamed to a TV. That's great for showing friends something that should be enjoyed in groups - the latest nonsensical music video or a collection of funny memes on Facebook. Airplay mirroring to a TV is a much better option than passing around a 4-inch screen. Nobody wants to take turns laughing.
The Chromecast extension doesn't mirror an entire computer but an individual tab within Google's Chrome browser. This method once again frees up one's computer to do other tasks while a background tab can stream to a TV. It also lets you keep the content of your computer private.
Unfortunately, you can't stream PowerPoint presentations or beam newly created pieces of art in Photoshop like you could with the Apple TV's device-wide computer mirroring capabilities. If it can't be seen within a Chrome browser extension, the it simply isn't visible.
Chromecast wins hands-down in the price department, costing just $35 (about £22, AU$37, though not available outside of the U.S. yet). Without a plethora of apps, the price is actually one of the best features of Google's media streaming dongle.
Even if no more apps are added, the Chrome tab extension is worth this affordable price. After all, most gaming machines and Roku boxes already have Netflix, HBO Go, Hulu Plus, YouTube and so forth, so native apps are actually a secondary feature here. Mirroring is much more interesting.
Apple TV, on the other hand, is a little bit more of an expensive "hobby" at $99 (£99, AU$109). It's a device that is worth $0 if you have an Android device or Windows PC without an unofficial workaround and just as inconvenient if you have friends with non-Apple devices.
Setup and connections
Both Apple TV and Chromecast are incredibly easy to setup thanks to their minimalist approach to connections on the back.
There's HDMI out, optical audio, Ethernet and power ports on the back of an Apple TV. It has a remote, but that's hardly even a necessity as iOS remote apps are just as functional.
Chromecast is even simpler, plugging directly into an HDMI port. It does require an external power solution via a provided USB-mini-to-USB cable and power adapter. The cable is six inches, so it should be able to reach a powered USB plug or outlet.
Chromecast is easier to set up, but for a few people who really want top-notch streaming speeds, it doesn't include an Ethernet port for a flawless hardwired connection. That may be a problem for households that typically experience router interference.
The silicon screen
The silver screen is giving way to the silicon screen as tech companies are taking over the living room. Now that Google has entered the fray with something worthwhile, Apple may invest more time and effort into its TV offerings with long-rumored Apple iTV.
For now, the two offer similar experiences with different ways of getting there. Apple TV can send more content to the big screen one of three ways: through native apps, Airplay or Airplay mirroring. But its slinging capabilities sometimes come at a cost of hogging phone, tablet and computer resources.
Chromecast has just four compatible apps and the Chrome extension tab on computers. That's convenient for streaming anything that can be seen within the Google-owned browser, but it doesn't work for programs outside of the web. It's a mixed blessing that it doesn't follow your computer around like the stalker-like Apple TV mirroring does.
What would really win the living room war for either couch potato-focused company is opening up Apple TV and Chromecast to grass roots developers. Google Play and the App Store are so popular because of the roughly one million apps available from the masses to the masses.
When that happens for Apple TV or Chromecast, it changes everything.