I would say that the Amazon Echo is generally better at DOING STUFF (e.g. setting alarms and reminders, playing music, adding stuff to your Amazon shopping cart (
of course), controlling your TV if you have a Fire stick, etc). Supposedly controlling smart home gear, although I haven't dipped my toes in those waters yet.
The Google Home is generally better at ANSWERING QUESTIONS and providing information. Random queries that pop into your head a thousand times a day (e.g. Who starred in such-and-such movie? Who won the last time the Atlanta Falcons played the Carolina Panthers? etc).
Occasionally though, Alexa will surprise you by answering a question where Google flopped. Either way, like others in this thread, I now have both since they discounted them so low for the holidays. But for the Google, I get by with the "Mini" version... whereas I sprung for the full-size Amazon Echo because I use it for music, audiobooks, podcasts, etc and want the better sound.