I've been told that the southern hemisphere hadley cell play a row to carry energy from the SH to the NH in the lower troposphere (elevation) whereas in the upper elevation, energy travel from the summer hemisphere to the winter hemisphere.
In a way, the Earth has two atmospheres, a Northern Hemisphere atmosphere and a Southern Hemisphere atmosphere. There is some mixing (and hence energy transfer) between them, but it's not a whole lot -- and the net energy transfer is from the Northern Hemisphere to the Southern Hemisphere.
The much greater energy transfer in which the Hadley cells participate is from equatorial regions to polar regions rather than from one hemisphere to the other. As the temperature gradient between equatorial regions and a polar region is much greater in winter than in summer, the Northern Hemisphere Hadley cell is more active in Northern Hemisphere winter than it is in the summer. The same goes for the Southern Hemisphere Hadley cell, except of course that the south's winter is the north's summer, and vice versa.
One key difference between the two hemispheres is that the Northern Hemisphere has a lot more land area than does the Southern Hemisphere. This makes the Northern Hemisphere warmer than the Southern Hemisphere, on average. It also makes the Northern Hemisphere more volatile, at least over land. On average, Northern Hemisphere summers are warmer than are Southern Hemisphere summers, while Northern Hemisphere winters are colder than are Southern Hemisphere winters. This is despite the fact that Northern Hemisphere winter and Southern Hemisphere summer occurs when the Earth is closest to the Sun, and vice versa for when the Earth is furthest from the Sun.
Another key difference is that the North Pole is in the middle of a small ocean that is almost entirely surrounded by land while the South Pole is in the middle of a continent that is completely surrounded by a not so small Southern Ocean. This difference again plays a role in the difference between the climates of this two hemisphere.
Why are the Hadley cells not symmetrical?
With all of these differences (seasons, land distribution, and the nature of the poles) between the two hemispheres, it would be very surprising if the Hadley cells were symmetrical. Not so surprisingly, they're a bit different.
