i like and use both.17hmr,17remington.on grays shot several coyotes with 17hmr.without an issue.also my old 788,222rem with 52gr hp seems fur friendly to me.
I blew out my first 17Rem fox using a 20gr Vmax (24.0 gr 4320 around 4100? fps). 45 yards lasered, shot head on in the chest. Dropped instantly with a terrible "thwack"! Entry hole the size of a golf ball, no exit.
While I love the .17 Remington, I have found it to be a bit too much for fox generally. Fox are very thin-skinned and it doesn't take much to put a large hole in the fur.
I have shot a few fox that have escaped the .17 with minimal damage, but most have good sized exits.
I have used only one bullet in the .17 Rem, the Hornady 25 gr. HP. There may be better bullets for fox, I don't know. If there are, I would like to try them.
I had considered a lighter bullet traveling faster, thinking it might go to pieces inside and not exit. I'm not sure that's possible with the .17 Rem, however, and your
photo and experience indicates that with the 20 gr. V-Max.