All centre fire rifles will kill fox, some bullets kill better than others with all calibers.
I have had 223, 22-250, and 243, when watching what happens after you have shot the fox what i have found is the fox will often riddle on the ground for a few seconds with the 223, a little less with my 22-250, and nine times out of ten just drop motionless with the 243 using home loaded Hornady 58g v-max doing around 3750 fps.
IMO the 58g hornady v-max kill better than the nosler 70g bt, but this might come at the price of shorter barrel life.
I wanted my 243 for maximum point and shoot range on fox with the best knock down power and IMO that is what i have got.
For anyone that's buying a new rifle, the same make of rifles are the same price irrespective of caliber so buy what you want.
Another consideration can be when shooting foxes around near by housing where noise can be a problem, my 22-250 is a LOT quieter than my 243.
Dave (warbucks)