We both Google home and Amazon echo.
And tend to rely on Spotify premium as that's the only service which works on both.
I don't think you can link Google play music to Alexa, or Amazon music unlimited to Google home yet
What is tricky though. Is arranging services so that both can be used in different rooms without trying to stream to 2 or more devices from the same music account. Especially because of how account selection works. Amazon echo. Alexa can only link to one music account , no matter who speaks. But Google home with voice match has a music account per person, plus a confusing rules for what to use for stranger's, for them It uses the music account of the 1st person who got to be voice matched. We can't set a default mussic account for strangersz that is different to both mine and my wifes. That would be handy as one Google home is in an apartment that we rent on Airbnb.
We have Spotify family, so 6 accounts to play around with. And still we get muddled. The home app will say this person has elected to use Spotify but will not say which of the 6 we assigned
Muddle in the fact that we also both have Spotify on pc, and Google music on Nvidia shield, and we will often cut off each others streams.
And with Google home, it does not say sorry. That account is already streaming, one device streams and the other just stops with no explanation.
Both services , both devices have a way to go to become truly family friendly
They really need to offer something like netflix 4 screens at once per account deal. Not one stream at a time maximum.
Also, Probably the legality of providing music on either device to paying guests is a total mess and requires a commercial licence, must like providing a dvd player and some discs, or a radio does. We take a don't ask don't tell approach to that mess and provide all of netflix. Prime video, Google home on streamers in our rental space. Using our own accounts plus pin for purchases protection on Amazon video
Our newest device is the jbl link view, their take on the Google home hub. Stereo speakers plus an eight inch screen.with Google assistant. Great audio quality. Way better then echo or Google home. It allegedly does video calls via Google duo, except we don't know anyone who uses duo that we can call ! But the grandchild can ask it to show kittens on you tube