With a correctly placed bullet, no crow or fox is having any say in the matter when hit with a SP, HP or plastic tipped bullet from a .222rem.
The more frangible the round is, the more apparent damage there might be. In many .224 bullets sold these days, they have plastic tips and are designed to fragment causing massive damage on impact. That is not to say SP bullets will not do the same. SPSX's were hilarious when I shot a few of those. They made things go pop such was the thin nature of those jackets.
I keep a couple of Sako 50grain SP's in my pocket when out and about with the .222 in case a Munty steps out. They will stop a fox dead with ease but will not do the same level of obvious damage to it as a 53g Varmegeddon.