The answer is, "not very", in the grand scheme of things. As has been said, past 75-100 yards, the wind drifts them a lot, and the drop becomes precipitous after 150 or so, so your holdover and range knowledge has to be immaculate. So the answer is really - it depends on the skill level of the shooter, both in range estimation and windage adjustment, the amount of wind and its direction, and what you consider to be "accurate". Don't expect teensy weensy groups much past 50-75 yards from the average to above-average shooter, with an average amount of wind, even from a really good rifle.
BUT...it's "all relative", of course - as they say. You said you're a handgun guy. Some "handgun guys" only shoot at 3, 5, and 7 yards. Some shoot at 10. Many shoot at 15 yards (45 feet). A few shoot at 25 yards (75 feet). Some shoot at all of the above. If you're one of those guys, like quite a few of the 'handgun guys' I see, who ordinarily MAX out at 15 yards / 45 feet (which incidentally is around twice the distance at which one would normally justified in using a handgun for self-defense rather than running away), then 50 yards (150 feet) is a long, LONG ways!! Well over 3 times the distance.
Even if you're one of those guys (like me) who like to self-induce head-banging and cursing by shooting 'standard' self-defense handguns at 25 yards, 50 yards is still a long ways (twice as much). And 75 yards is 3 times as much as a very, very long handgun shot! (Now granted that you're ordinarily gonna have a rested shot from the rimfire rifle vs a freehold shot from a handgun, of course).
So to my way of thinking, 75 yards (225 feet!) IS in fact "long distance shooting" for a 'handgun guy' (and/or, for that matter, for a .22 rimfire, for any guy or gal), in the relative scheme of things (as opposed to the grand scheme of things). And yes, a .22 rimfire can make reasonably good groups at that range - enough to put a smile on your face. With a good rifle and good shooter (knowing your drop and a little kentucky windage), you ought to be able to get 10 shots inside of 4 inches at 75 yards - good enough to take out a cottontail consistently.