Here is what I have so far for comparison. The list of commands is very similar between the 2 devices from what I have found on-line. Echo users feel free to correct me if any of this is wrong.
** Things that they both do (or probably do) very well:
Have excellent active listening mics, even in noisy rooms
Answer basic questions very well / search for information (what’s the weather? Math questions, check sports scores, etc.)
Play music via voice commands. Pause, restart, skip, change volume all with voice commands.
Also incorporates physical pause /play / volume controls
Decent sound quality from a relatively small device
Set timers and set alarms via voice command
Add items to your default shopping list
Request word translations
Play simple “easter egg” games
Control smart home devices
** Things that the Echo can do that Home cannot do (to the best of my knowledge):
Multi-user support. The Home currently only recognizes the calendar, shopping list, playlists, etc. for the main user that set it up with the Home app.
Add additional speakers for multi-room music. Google says you can connect multiple Home devices together in separate rooms, but that's expensive. No “Dot” style devices yet.
Order items directly from Amazon, and track packages via voice commands.
Offer a remote for audio controls when out of voice range.
** Things that may be unique to the Google Home (to the best of my knowledge):
My Day. Say OK Google (or Hey Google)…tell me about my day and she will read top stories from the news service of your choice, list calendar events and reminders, list the current weather and forecast and commute to work information.
Cast a song to any connected Chromecast music device via voice command.
Cast a You Tube video to any connected Chromecast device via voice command.
** Things that I hope Google fixes or releases soon:
Multi-user support. It’s a connected home device so it needs to be able to recognize multiple family members and read their calendar, play their playlists, etc.
Release small, inexpensive connected speakers so you can have mutli-room support.
When casting a song to a Chromecast music device, be able to hear the music on both devices simultaneously. Currently when you cast from Home to a Chromecast the song stops playing on the Home. I want to be able to hear it in both rooms at once.
Read shared calendar events out loud. Currently, Home will only read the main calendar for the user that setup the device. I have a shared “family” calendar full of family appointments and it should be able to read those also.