Having shot in excess of 100 deer with the .22Hornet, .223Rem, and .22-250; I think I can anwser your question.......
In distant past, the bullets were generally much poorer than we have today.
Now, read carefully what I'm relating.......
With the .223 and .22-250 (or similar .22cf's) use at least a 55gr Pt.Spt bullet, preferably 60gr or heavier. I lke the Sierra and Hornady offereings. The Noslers are much more expensive and likely don't offer a significant improvement in .22"
Place shots well......... This is most important..!!!!!
I've killed a number of deer with the .243WCF as well. For statistical purposes, I've had better results with the .22cf's due to bullet failures with the .243. In reality, there is little difference between a 60-70gr .22cf and the .243 with 80-100gr cup and core bullets. Both can kill DRT, and both can cause lost deer with poor shot placement.
Losses of deer with the .22cf's (my experience) are due to same reasons as deer lost with .30'cals. Poor shot placement!!!!!!
I lost more than my normal average this year, even though I DIDN'T use a .22cf. Lost one with a .257WBYmag. (bullet failure-115gr Nosler BT blew up on a shoulder shot @ 90yds w/3,550fps mv.) Other was a poor hit (too high to shoulder) with a 200gr Rem Corlelokt @ 2,300fps mv @ 195yds. Both deer were located several days later after coyotes and vultures had done their thing.....
If I'd been shooting a .22cf, both would likely have dropped DRT to the shot, since both my larger .22cf's shoot 1/2moa or better and shots would have been better placed...........; and performed better when they arrived.. (the 200gr Corlelokt is superlative, but still has to be placed properly............