I am relieved (and even quite pleased) at the general good sense displayed by my fellow respondents on this worthy thread. Most appear to agree that it is really a "Horses for courses" affair and each caliber and chambering here has its RIGHTFUL place in the scheme of things, dependant on the rabbit/fox ratio on one's shoot and the ranges at which these two target species regularly present. I have even used my .22K-H on the very occasional and opportune Munty, though that is quite rare. But it kills quickly and with some authority when ranges are close and P.O.I. carefully selected.
I am guessing there are those that have done similarly with a .17HMR but you wouldn't get me trusting such a light weight, frangible round at close quarters and CERTAINLY not at any range where I just might take on a fox if I thought the shot ethical(??).
All things taken into consideration I believe it would be difficult to disprove the slightly better overall abilities of the .22H (or .22KH slightly more so) over the .17HMR. I have and often use my .17Rem c/f with 20gr V-Max over CFE 223 propellant at a MEASURED 4450fps average velocity give or take about 30fps or so and it is truly devastating on rabbit and fox out to 250yds and beyond so this makes a great foxing round at night as my lamp, though pretty powerful, only really gives me about 150 yds or so of clear identification level illumination - with the eyes shine-back WAAAY more distant than that. However, my .22KH tends to be my goto rifle given the ranging limitations at night, and I am perfectly happy with that!..
ATB ....... and shoot safely