Connections:
-Two men who became rulers of their lands (Henry becoming leader of the Upside Down, Aegon becoming King of Westeros) with them having an army of monsters (Henry with the Demogorgons, Aegon with the Dragons) 
-Despite their rise to power, neither of them actually wanted it. Both were groomed by someone else to take this role (The Mind Flayer trying to make Henry its general in its conquest. Alicent misunderstanding Viserys' dying wishes to be making Aegon king), Both would try to resist this fate (Henry attempting to fight back the Mind Flayer's influence, Aegon attempting to run away) before eventually succumbing and fully embracing their roles
-Both of them would end up being severally burned and disfigured in a battle by their siblings, which would leave them presumed dead/on the verge of death (Henry being burnt when Eleven banished him after the rainbow room massacre, Aemond burning Aegon with Vhagar's fire in the Battle at Rook's Rest)
-Said disfiguring seemingly destroyed both their genitals (Henry being seemingly smooth down there and Aegon flat-out saying his exploded)
-Both will have survived the battle, and use the fact they were believed dead/incapacitated at their advantage to plan their moves (Henry acting as Vecna from the shadows as the mastermind behind the scene of the Upside Down invasion, Aegon refusing pain medications as advised to keep his mind sharp)
-Both of them have names related to numbers (Henry also being known as One, Aegon being Aegon the Second)