Stainless has one particular benefit over other materials: it is extremely predictable during its predicted lifespan. Beyond that it may fail unexpectedly, and usually catastrophically.

Bronze is less predictable, but is much more resistant to fatigue. For this reason the metal of a bronze turnbuckle is heavier, but bronze is more popular in most applications other than where weight is more important than longevity.

Chrome is nearly solely for appearances. Bronzes will slowly corrode to a sea-going green unless regularly polished, leaving the bright portions indicating use. Chrome will itself wear off through friction and use; fittings can be re-chromed. I don't know if chrome will indicate fatigue cracks of the fitting, but I would expect so.