Home Assistant is the big one, biggest community, most integrations, you can pay for their cloud stuff to get easy integrations to the big corps above. They also have a dedicated device they sell you can use to run HA.
Domoticz is a bit of an odd bird, I never figured out what was their value propositon
OpenHAB is the one I'd pick if I had to install a system for someone else than myself. It's not exactly easy to configure (the object/entity structure is a bit weird IMO), but it has a pretty decent amount of integrations and it's rock solid German engineering made with boring old Java.
If you want control, my suggestion is to use HA only for the integrations and do all of the brains somewhere else. Either a self-made program that pokes HA using its API or directly via MQTT or Node RED.