You can actually still use google Home if you want to - it integrates well with Google Home and Alexa but is currently massively expanding their own voice assistant option.

Home Assistant is more a "background" integrator - it links up all you different smart home options, makes them thereby smarter and adds external data (e.g. weather, traffic,etc.) whenever you want. And of course enables you to easily add your own visualisation and your own automations.

It is on one side incredibly easy to "start". And on the other side incredibly powerful.

Philpo explained it well.

I’m currently using Home Assistant as my integration platform to talk to everything, and as an automation engine to make things happen.

Home Assistant can then expose your devices to other platforms like Apple HomeKit and Google Home.

For controlling things manually, I mostly use the Apple Home app, and Siri and Google Assistant for voice control.

This year the Home Assistant developers are focusing heavily on building out native and local voice control. There will be an announcement in a week on their progress. It looks like they will be announcing the ability to use wake works to activate voice commands (like Google/Siri/Alexa but all done without compromising your privacy).