there are actually several things at play, eccentricity, precession, and obliquity. the net result is that the north gets milder winters and cooler summers.
the northern hemisphere has significantly larger temperature variation than the southern
the net result is that the north gets milder winters and cooler summers
One of these statements appears to disagree with the other. If I remember correctly what I've read, the proportion of land rather than ocean in each hemisphere plays a major role in climate, as mentioned by the reply saying that the Northern Hemisphere has more variation in temperature.