The Google Home assistant is not too bad overall, and it's definitely the right choice if you are heavily Google-dependent.
Thanks to their expertise in voice control, the guys at Google managed to teach their assistant to recognize different Google account owners by the sound of their voice. If both you and your girlfriend use Google Calendar for example, the Home will be able to read your respective meetings in your personal accounts. Other Googleries such as Maps and Keep are connected too of course.
If you're into smart-home control however, the Home isn't quite as good as Alexa. It doesn have some integrated capabilites, as well as some actions comparable to Alexa's Skills, but not as many - although it's catching up.
Chromecast users are going to love the Home. It can control Chromecast Audio multiroom systems, meaning you can ask it to stream music to speakers placed in different rooms symultaneously.
When it comes to day-to-day use, I don't find the Home as smart as Alexa. Even adding an event to your own calendar is kind of needlessly laborious, and the lack of Skills makes simple tasks harder.
In terms of other device choices, a Google Home Mini, a higher-end Google Home Max with an integrated speaker system, and a Google Home Hub (with video) are available.