The .22 Hornet and .223 are really not in the same class, albeit both .22 calibres. It is akin to comparing apples with pears; both fruits but very different.
I support the use of the Hornet out to 150 yards, further than that and I struggle with trajectory. It will kill foxes as far away as I can hit them, which is about 150 yds.
The Hornet is much quieter, particularly if used with a moderator, has no perceptible recoil but arguably is less flexible as it cannot lawfully be used for shooting the smaller species of deer. Richard Prior himself is on record as having shot numerous Roe with the Hornet before it became unlawful to do so. It is a very powerful round, in it's own right.
Much nonsense has been written about the Hornet being difficult to reload, you just need to be careful and gentle, particularly when seating the bullet. If you use the Hornet on rabbits and hit them in the body, then there is little to compare with the mess made by Hornet, .222 or .223. All make a big, bigger and biggest mess respectively.
I love my Hornet, but it is no .222 or .223 and I have owned, reloaded and used all three cartridges. Whatever you decide, enjoy your quest and the sport.