In preparation for a podcast that I will participate in this weekend, I am thinking about my experience with Google Home.
Google Home does not have much that is better than Echo, which isn't too surprising given Amazon's year+ lead over Google. Home excels in Internet search, as you would expect, so it is a bit better for finding general information.
Another way that Home is better than Echo is its ability to control Google Chromecast. First, Home automatically finds Chromecast devices on your home network, whereas you need to explicitly set up other home automation devices like Hue and SmartThings.
Once you get Home connected on your network, you can say things like, "Ok Google, show pictures on basement TV" and Home will start a slideshow of your Google Photos on the Chromecast called basement TV. You do need to have the Chromecast running on a TV before seeing the pictures, Home will not turn on your TV unless you have it integrated with other home automation devices.
The speaker built-in to Google Home is slightly better than the one in Echo, but both are pretty good. Neither are as good as the Yamaha soundbar I have connected to my Samsung TV, so I enjoy telling Google to play my favorite music on my Basement TV Chromecast, which of course sends audio to the soundbar.
I have Google Home and Echo connected to my Spotify account. Of course Echo plays music from Amazon Prime as well as any music that you own and associated to your account. Google Home also plays music from Google Play, where I happen to have uploaded all of my personal music that I ripped from CDs over the years.
Home also is integrated with Netflix, so you can say "Hey Google, play Supergirl on basement TV" and it will start streaming via Chromecast to your TV. I can configure Echo to turn on Netflix via the Harmony hub, but I cannot direct it to a specific show, although I can tell Harmony to turn on specific cable TV channels via Harmony.
Alexa, which is the brains behind Echo, has a ton of skills that add functions, ranging from the silly, like telling jokes, to requesting an Uber. Amazon has a pretty good developer network and seems to be releasing new skills for Alexa every week.
Home has services that add functions, but only a few are currently available. Most services are basically a form of a web search but there are services like Uber, Todoist, and Kayak that provide specific functions.
Echo and Home both work with If This Then That, so you can use them to trigger applets that work with other smart home devices or web services. I am surprised that there is no real integration between Android and Google Home, but you can add it with Tasker and AutoVoice, which are automation tools for Android.
Google Assistant is the brains behind Home in the same way that Alexa is the brains of the Echo and Dot. Assistant is also available on the Google Pixel phones, while Google Now is a similar, but not the same, assistant on all other Android devices.
Google Home ought to be able to recognize Android devices just like it does Chromecast, and likewise Android should know about Home. Here is a an example of where the lack of integration causes a problem.
I have Google Now configured on my Nexus 6 P to wake up whenever I say "Ok Google" even while I have the phone turned off. When I am in my basement and say "Ok Google" both Home and my phone acknowledge the wake word. The phone should recognize there is a Home nearby and defer to it, just as it does with Android Wear, but it does not.
Even more maddening is the integration with Keep, Google's notetaking and list making app. Home/Google Assistant creates a item in Keep called Google Assistant shopping list, and you call say "Ok Google, add milk to shopping list" and Home will add milk to that shopping list note.
Say "Ok Google, add bread to shopping list" to your Android phone and it will add bread as an item to another entry in Keep called Shopping List, which means you end up with two shopping list areas in Google Keep, one controlled by Assistant/Home and the other controlled by Google Now. How hard would it be for Assistant to add items to the Shopping List entry that Google Now uses?
Oh, and by the way, Echo also has a shopping list that is of course directly connected to Amazon so Alexa can automatically order stuff on that list, where as the Google's shopping list is more traditional.
The duplicate shopping list scenario is the type of thing we see with first generation products like Google Home. I expect Google Home to get much better as Google improves Assistant, which I think will ultimately replace the Google Search web page. In the mean time we will have to wait and see whether Google Home will surpass Amazon Echo.