How can I compare a TVS diode with a varistor?
Varistors are "baked" semiconductors, their properties aren't tightly controlable. Think of them as a mesh of billions of Schottky junctions. Their big pro is they can both short a spike and turn it into heat smoothly because of the high mass of the actual mesh.

In addition, as the varistor heats up, it gets more conducting and this can be used to blow a fuse for the case the overvoltage is not transient but steady. When the overvoltage is gone, the user replaces the fuse and the device can be used again.

You cannot do this with a TVS as it would blow before a fuse could react. You had to limit the current through it some way. Usually, this means you are using a TVS only on signal lines where the current is limited by the existing circuit itself.