I am just starting my journey with the Hornet. I am shooting with open sights at the moment. Next job is finding some dies and start working up a load. Factory ammo seems to be hard to find and expensive.
My reckoning so far is the Hornet is big little cartridge, whereas the 222 and especially the 223 are little big cartridges.
The Hornet is a 150 max cartridge and it tops out at Fox, small antelope, marmots, racoons, black grouse etc. and suspect its really useful in Europe, Africa and the Americas.
In the UK I think it’s the optimum cartridge for Hares.
The 223 is a bit too powerful for rabbits etc, if you want to eat them, and perfectly capable of shooting pretty much any medium sized deer or antelope, and certainly very capable on predators other than the big cats and bears. And its perfectly capable out to several hundred metres.
You probably want a bigger rifle for many of the above, and almost certainly will for legal reasons, but if you have a 223 with good bullets and take your time to place the shot correctly it will more than adequately do the job, as it does every day all around the world.
22 Hornet will also do, but I suspect you would be much more reticent and / or get in very close and would really prefer something quite a bit bigger.