My 2 cents would be to get the .223.
The main reason would be for the 1:12 RoT, secondly would be the better availability of components, and finally would be the accuracy.
Not to say that you can't kill deer with a 22 Hornet, but you would probably need to hand load for it as the factory ammunition is all geared towards light varmint use.
I have personally used my CZ 527 in .223 to kill something like half a dozen deer, a couple of antelope, and one cow elk. Depending on what your rifle likes, I would recommend using either the 53 gr Barnes TSX, the Nosler 60 gr Partition, the Hornady 60 gr InterLock, or the 55 gr Remington.
In general, the 1:12 CZ rifles tend to like the lighter weight bullets with harder jackets. But out to 100 yds, 3/4 MOA will give you enough accuracy to take the necessary shots.
Where the .223 shines in in the precision it offers and the ability to maintain your sight picture after the shot.
One word of caution on the TSX, though, is that it needs to hit bone to work well. Otherwise it will behave like FMJ and just pencil through. So, shoulder and head shots are what it is best suited for.