[Melkor89]

The army that would claim victory in a war between Gondor and Rohan is not apparent. It all depends on what kind of war it was. If there was a siege of Gondor, Rohan would be beaten down pitifully. Minas Tirith is a huge city from which the inhabitants can defend themselves as well as keep massive stores of supplies. Although Helm's Deep can do this also, I was under the impression from reading the book that Helm's Deep was smaller than Minas Tirith and would have less room for supplies.

However, if the armies of the two kingdoms met outside of their main fortresses, Rohan would have the upper hand with their superior horses and riding skill.