This deserves a more careful answer than it usually receives, because the two materials behave differently above and below ground level.
Hot-dip galvanised steel carries a zinc coating that protects sacrificially: the zinc corrodes preferentially and the steel beneath stays intact. This works in soil as well as in air, which is why galvanising remains the default choice for buried applications. Coating thickness determines service life.
Corten (weathering) steel forms a stable protective patina only where it experiences alternating wet and dry cycles with free access to oxygen. Above ground it performs exceptionally, and the patina is self-repairing. Below ground it does not form that patina. Permanently damp, oxygen-poor soil prevents it, and the buried section continues to corrode.
This is not an argument against corten posts — it is an argument for understanding where their advantage lies. Corten’s benefit in a vineyard is the aesthetic of the exposed section and the material’s higher strength, which allows equivalent performance at reduced section. For the buried portion, what protects the post is wall thickness and, where specified, an additional coating.
Vineyards in coastal or permanently wet sites should specify galvanised below ground regardless of what is chosen above it.