Home Assistant is open source home automation that puts local control and privacy first.
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Home Assistant can be self-installed on ProxMox, Raspberry Pi, or even purchased pre-installed: Home Assistant: Installation
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There will be many different takes on this subject, but IMO the most important concern is device availability.
I use Zigbee because then I can install Hue, Aqara, IKEA devices ++
If Zigbee devices are hard to get where you are, definitely go for ZWave.
I have both and use them with home assistant. Personally I don't have a preference and I just get the best device for my needs as long as its one of the two technologies. The only knock I have on zigbee is one of my sensors likes to continually drop but that's probably a problem with that particular samsung sensor and not a problem with zigbee as a standard.
As far as HA integration goes, I don't think either is better than the other in my experience. They both work perfectly (other than that one sensor) and were easy to setup. Personally I'd say figure out what devices you're likely to want in the future and then see how many are on zigbee/zwave, their costs and reviews and availability, and just choose one. Can always add the other later on for relatively little money if the need arises.