At the end of the day, both will provide you with good service. It is best to make your decision based on how much you will use your trailer and your budget.
Opinions vary on this subject and are based largely on personal preference.
Leaf Spring
Leaf spring axles are the most common axle found on trailers due to their affordability. They have flat, curved leaves stacked on top of each other in several layers. The leaf springs themselves are attached directly to the trailer frame, not the axle.
Although they may need more maintenance than torsion axles, their parts are replaceable .
If a tire on your trailer goes over a pothole or lower place in the road, other tires on your trailer may not remain in contact with the road surface. This is because the leaf springs do not function as independently as torsion axles.
Torsion
Torsion axles are attached directly to the trailer frame thereby providing more trailer rigidity. This method of attachment also reduces flex in cross winds and on rough roads.
They have adjustable ride height and a rubberized suspension system. Inside the axle housing there are four rubberized cords. As each wheel moves up and down, the rubber cords compress resulting in an even wheel suspension system for a smooth ride.
The axle tube is galvanized inside and out to reduce the chance of corrosion and there is no metal-to-metal.