So at this point in the game, he had Cavalry and not his Mandekalu Cavalry UU? The UU is a knight replacement, while the Cavalry unit has 25 combat strength and is a Renaissiance unit. Major difference there; if Cavalry, then it would seem like you are at a tech disadvantage to him, which takes a lot of effort to overcome.
Regardless of what he's using, pikemen and Keshiks are the way to go. If you are invading his territory but not getting anywhere, I'd suggest moving your troops back into your territory, then build up a large force of pikemen/keshiks and renew the assault. If you have any ranged units he shouldn't be able to take any city of yours, so all you have to do is build up a superior army, crush his, then take cities one by one.