Both are designed to be primarily voice controlled - Google Home lacks buttons altogether - and to blend into most decor.
Inside, there's WiFi along with a speaker and microphone array; Amazon is particularly proud of the seven microphones that give Echo its precise ears, though it's hard to imagine that Google hasn't given across-the-room pickup the same sort of consideration for its device.
Unlike Echo, which is music-only, Google Home will support video streaming too: you'll be able to verbally search for a clip, movie, or TV show, and then have it beamed over to a TV with a Chromecast plugged in.
Some of the spoils of that were shown off during Google Home's brief demo: answering questions that, I suspect, would've easily stumped Alexa.
I enjoy Amazon's virtual assistant, but her ability to muster up solutions is rudimentary: if she can find a Wikipedia entry for it, you're usually good to go, but anything demanding a more intuitive take gets you "I'm sorry, I don't understand the question" at best.
It's also data that, though Amazon could try to help you duplicate, it faces a considerable barrier with: people's inherent laziness when it comes to jumping platforms.