I have two Google Home devices and two Alexa devices (both of my Alexa devices that are third party devices and not produced by Amazon; Zolo Halo and Eufy Genie).
From my experience, I GREATLY prefer Google assistant over Alexa. Using Amazon skills is really clunky compared to Google home and half the time Alexa doesn't want to work with my stuff even though I have my stuff paired with both assistants.
Google assistant is smarter and more accessible to me since she is on my phone and my Android Wear Watch. The lack of Alexa on wearables and phones (except for a few fringe cases) will hurt Alexa integration into daily life enough for Google to surpass her in popularity and market share.
Also add to this, Google has ALL of our browsing history, trends, etc at their disposal and although Amazon has their platform and search history, it pales in comparison to the amount of data Google has to produce a smarter assistant.