I feel like it would have to be Gondor, (assuming we are talking about LOTR time), Gondor was a greater kingdom, but if you took all their men I think they would outnumber Rohan 2:1. So long as they didn't try and charge the Rohirrim on an open field then that takes away Rohans real advantage, so I would definitely back Gondor!
a bit like the dothraki vs the knights of westeros
In theory I agree with you the men of gondor generally have better armour and have a bigger force. however I feel that the harshness and wildness of rohan has made the men braver and fiercer than those in gondor. so while i agree that in a city or a siege i thing gondor has the edge, in any other conflict i think rohan and their horses have a massive advantage. I could be bias though as i have soft sport for rohan being originally a country boy myself.
Gondor, if it isn't in an open field, otherwise Rohan would crush Gondor
At Gondor's peak I have no doubt that they would win. However, Gondor was already past it's prime when Rohan was given to the Éothéod.
I think it would depend on the circumstances at the time of the battle. If you're talking about the armies in context to what they were like in the movies well, Gondor would literally be a doormat to the Rohirrim. Don't get me wrong, while the Gondorians are quite a force to reckon with, they were fighting Sauron's minions on a daily basis. They were exhausted, worn down both emotionally and psychologically, their numbers were dwindling rapidly, and they were completely terrified of their enemy - you could see it in their eyes. They seemed, at the best of times, dazed and confused. Quite understandably so. Now, if you rest them, feed them, repair them, and give them a very serious pep rally before sending them to battle, then we would see their true might.
On the flip side of that coin, the Rohirrim were used to fighting somewhat minor random skirmishes, throughout their hold. They did not fight on a daily basis. They were actually out looking for a battle and they did not have the fear that the Gondorians had. They always seemed fresh and ready to go.
Outside of that, and personally, I think the Gondorians and the Rohirrim are on equal footing. Both armies are extremely skilled in their respective fighting forms. Both armies had horses, though the Rohirrim are much more skilled at riding. Then we look at their armor: the Gondorians have heavy metal armor which is great for protection and can be somewhat intimidating to their enemy, while the Rohirrim appear to have lightweight, mostly leather armor, with metal breastplates, that can be damaged more easily but, also gives more freedom/ease of movement than heavy armor does. Both have metal helms. Next, while the Rohirrim may be more skilled at horsemanship, I think the Gondorians can clearly hold their own. The Gondorians and the Rohirrim can both fight equally as well on the field as well as in a besieged situation. They are both quite adept at battle strategies and at fullout charging into the oncoming enemy. If we take them off of their horses, we have, what "I" would call, the equivalent of Viking Berserker meets Roman Legionaire. A very equal match. A stalemate. Lastly, if we look at the numbers, Gondor may have the larger army in mass size but, numbers are not everything. Brute force alone does not win a war, there is always strategy at play. Always! and on both sides. Both the Gondorians and the Rohirrim are quite strategically capable. These are the reasons I believe they are equals. Just like the Viking and the Legionaire - a stalemate.
This is, of course, just my own perception of their abilities in a battle against each other.
What I'm saying is that, at the end of the battle, they would look at each other and each say "we have met our match", then they would shake hands, call it a day😉, and then the Rohirrim would show the Gondorians how to party. 😂