The primary advantage of model checkers is that they are relatively easy to use and produce counterexamples when a property is not true. Their main disadvantage is that even moderately large models can still exceed the capacity of the model checker.
Theorem proving is a technique where both the system and its desired properties are expressed as formulas in a mathematical logic, and these properties are shown to hold through use of a mechanical theorem prover. While theorem provers do not have the state space limitation of model checkers, they generally require more skill and labor to prove the desired properties.