To show that an argument is invalid via models, you need to consider every model; to show that an argument is valid via proofs, you need to consider every proof.

Model-theoretic methods don't make use of structures, while proof-theoretic methods do.

It just takes one model to show that an argument is invalid, and it just takes one proof to show that an argument is valid.

It just takes one proof to show that an argument is invalid, and it just takes one model to show that an argument is valid.