With two Hadley Cells
The Hadley Cells would expand and contract with the seasons.
The winter cell would stay put and intensify its circulation of air due to the higher degree of temperature variance from the equator to the poles. The convective updraft region for this cell would be narrower, but more intense, and would be focused near the equator. It would still flow from east to west like our own Tropical Convergence Zone, but much slower, and might meander a little bit into the other hemisphere like our T.C.Z. during the winter.
The summer cell (for this lets say the northern cell) would migrate poleward a bit, widening and weakening the updraft region as it goes.
A lot like the jet stream in some respects:
As it moves farther north, the convection behind it would weaken and be pulled northward as the air behind it starts to descend. Spin off low pressure systems would kink up the weaker band of updrafts into knots and loops until it hardly resembled a band at all. As this happened the belt would slow down and would probably at some point change direction from east-west to west-east due to the weak but still present Coriolis effect. Warm tropical moisture flowing from the south could form some powerful storm systems rotating any which way where they encounter the cooler air of the north.
Meanwhile down close to the equator if a tropical system initiated and had enough spin to break from a tropical wave, a hurricane could form. It would meander a bit, not pushed as much by the Coriolis effect, but by the flow of air from the Hadley cell northward where it would eventually slam into the disorganized convective belt. This would push a large region even further northward in a bulge and would act to intensify the belt as a whole, contracting the updraft regions and forming powerful winds. On this planet you could also have two hurricanes form, side by side in the same hemisphere, but rotating in opposite ways.
If the Hurricane formed too close to the equator it would be trapped against the equator by the air rushing from the high pressure to the north and south. Conceivably, this hurricane could jump hemispheres back and forth across the equatorial band like a kid playing hopscotch until it hit land or was killed by atmospheric turbulence.
Tornadoes would still form. But super-cells which form the most powerful tornadoes would be more rare as they require both upper level and surface level wind shear to form. This planet simply doesn't have shear like that on a regular basis. Landspouts and waterspouts would still be common though as wind shear is not as important in their formation. And even more than the hurricanes, the tornadoes wouldn't really care which way they rotated.
I am not quite sure how far north this belt would go. That depends on many factors. It could conceivably go as far as 60 degrees north or even to the pole before making the trek back down.
Titan's updraft belt at the pole:
The temperate latitudes would receive the majority of their rainfalls in spring and fall when the band moves overhead. Summer would be mostly dry except for occasional monsoon thunderstorms. Winter would also be dry, but very cold and windy.
The sub-tropics would receive rainfall starting in spring as the band moved overhead, continuing into summer as typical tropical thunderstorms and then again in fall as the band moved southward. Winter would bring only occasional rainfall.
The poles would receive its only real precipitation in summer when the band is at its closest. The rest of the year there is a huge downdraft over the pole that pushes cold air across the landscape and toward the equator. In winter the cold would be especially harsh, as would the winds.
At the equator the rain would be nearly constant like it is here on Earth.
In the tropics rain would fall steadily for half the year, and then would receive rather chaotic rainfall depending on the strength/position of the migrating downward moving air, and the proximity to the other band of updrafts.
In winter at ground level the air would flow from the poles toward the equator but curve more toward the west as you get closer to the updraft band. On the equator winds would be out of the east flowing toward the west.
In summer as the band passed by air flow up from the south would be quite strong. This would gradually weaken as the band moved on and air started descending behind the band. The southerly flow would continue until the band passed by again.
However, on the equator side of that downdraft, the air would flow from the north down to the equatorial band. The descending air instead of flowing toward the band, would rush away from it toward the equator until it rose in the wintertime band.
During the band's trek winds would be chaotic at ground level due to mixing cyclones from the north and south along with convective downdrafts.
Dry and Wet areas:
Depending on how far toward the poles the band of storms moves, and how long it parks there during the summer the poles could either be desert, or rainforest. Assuming that Titan's band of storms remains over the pole for longer because of its greater axial tilt of 27 degrees to our 23.5 our poles would be much drier. In fact, they would probably be something like a cold version of the African Savannah except for the extremely high latitudes where it would just be barren. This is just the average, seas, mountains, and polar oceans would greatly alter this recipe.
The mid latitudes would most likely be the driest due to a rather rapid transition of the low pressure band from the sub-tropical latitudes to the higher latitudes. This combined with the weakening described earlier that the low pressure band would undergo could make the mid-latitudes semi arid on average. Large mountain ranges oriented from east to west would be much wetter due to the warm humid air coming from the equatorial regions in summer, and the cold snowstorms that would form on the poleward side in winter. This would effectively create rainforests on the equatorial face, and deserts poleward from there.
The sub-tropics would be similar to ours, with just a tad bit more rain. Instead of a 6 month dry season and a 6 month wet season like ours, there would be a wet season 3 months long, separated by a 2 month season with a mix of wet and dry, then another wet season 3 months long, then finally a 4 month dry season.
The equator would be very similar to ours, but probably with more wind and more rain. If the wintertime Hadley Cell migrated a bit into the other hemisphere then the equatorial region would have two seasons, a wet season, and a dry season.
Hot and Cold zones:
It would still be hot around the equator. But most of the worlds deserts would be in the mid-latitudes nestled in mountain shadows or far from sources of moisture. These locations would probably have your greatest temperatures.