Round nose bullets "hit harder" on game as they create a larger temporary wound cavity upon impact, as compared to pointy bullets. They also let you increase the weight of your bullets without increasing their length as much as with a traditional spitzer. Lots of rifles seem to prefer them for accuracy too.
For under 200 yards they're deadly. I've used them in my 338 win mag when going into the bush after game that was hit, but didn't have the decency to just fall right over and die. My father uses them in his 375 H&H at close range, as well as 220gr RN in his 303 British on the trapline.