Zhuge Nu are not very good against Yeoman because Yeoman have more range and more movement speed, allowing them to kite Zhuge Nu easily.

Palace Guards against a civilization like the House of Lancaster with very expensive archers, where typically you just want to be pumping out melee infantry. They do quite well. They've got three melee armor, only two ranged armor, but the three melee armor, especially against both Hobelar and Spearman, mean that you have a very, very tanky front line with them.

The three pierce armor on the Hobelars really heavily counters the ability to make Zhuge Nu even remotely viable, which is a problem given that they have no option for archers or anything else either.

The Lords of Lancaster, not only are they really tanky, but they also have a lot of base damage. So even the three armor on the Palace Guards doesn't mean that much.