Who to give close counter to?

Armor Emblem is better than Flier Emblem, so if you're running a themed team, definitely H!Henry. Slap Owl Tome on him while having other Armor Units supply Ward buffs and he slays, completely.

Outside of these teams, it really just matters as to how the fit into your teams. Henry still is a superior unit, but that doesn't mean it is best on him in the context of your team. I, personally, would save it or slap it on a buffed Arvis.

Personally, I'd say S!Camilla: due to Henry's -def, I feel he'd be much better off as an offensive mage even in armor emblem, and Camilla has very respectable bulk regardless. Back a few months ago CC Gronnblade Vantage Camilla was popular, so you could go with that.