This is what happens when you have a heavily industrialised(for the time) part of the country fighting hillbillies in a minor territory with little room to maneuver. Plus, the victorious "Sonderbund"(special alliance) was led by Guillaume-Henri Dufour which said:

Il faut sortir de cette lutte non seulement victorieux, mais aussi sans reproche.

roughly:

Not only must we leave this struggle victorious, but also without reproval.

It may not surprise you that he later became one of the founders of the international red cross.

You could write whole books about this war but as a TL;DR:

In the initial stage small militias clashed into each other with little effect and few casualties. The number of casualties was low because both sides lacked not only the equipment and training to attack(artillery was still in the armories), but also to chase the beaten enemy(regular cavalry units needed some time to assemble).

Once the Sonderbund threw its army onto the field the war was already lost for the Catholics. The Sonderbund was better equipped, more numerous and had a better command structure. They beat the catholics in three battles, overruning the positions. While cavalry was on the catholics heels all the time they merely tailed them and caused disturbances, but did never directly attack. This allowed the catholics to retreat, but they could never assemble all their forces on the battlefield, leaving the forces arriving there heavily outnumbered and under heavy concentrated artillery fire. This in turn led the troops to rout before they assembled properly, and when they ran away they had to deal with the cavalry again.

The whole thing was really a masterpiece of warfare and it was an absolute necessity to fight the war with as few casualties as possible to ensure a future for Switzerland.

If you ever a book on the Sonderbund war, read it! It's totally worth it.