This is just personal experience. I have both google home and alexa (plus a dot). My observation for my use:
1. Google responds more to my command with slightly (not much) more natural tones;
2. Google recipe for cooking (I tried only once) is tremendously more helpful with waits and timers automatically added on;
3. Alexa has better sound for music although I only listen for working background not for serious music listening;
4. If you ask Google to say hi to Alexa it does whilst Alexa would say a long blurb about your contact skill is not available blah blah. But she responds to Google's greetings;
5. Calling "Alexa" is just easier than calling two words "hey google";
6. When Alexa skills work, they are awesome but it really is annoying to remember all the cues for skill names which i don't.
Overall, they are both very limited still. Right now I use Google a little bit more. It probably also helps that Google knows everything about me given I work in front computers all day but not so much with Amazon.
1. Google responds more to my command with slightly (not much) more natural tones;
2. Google recipe for cooking (I tried only once) is tremendously more helpful with waits and timers automatically added on;
3. Alexa has better sound for music although I only listen for working background not for serious music listening;
4. If you ask Google to say hi to Alexa it does whilst Alexa would say a long blurb about your contact skill is not available blah blah. But she responds to Google's greetings;
5. Calling "Alexa" is just easier than calling two words "hey google";
6. When Alexa skills work, they are awesome but it really is annoying to remember all the cues for skill names which i don't.
Overall, they are both very limited still. Right now I use Google a little bit more. It probably also helps that Google knows everything about me given I work in front computers all day but not so much with Amazon.