Anyway back on topic, I've actually never played any of the stronghold games... not sure what's better/worse than Age of Empires but I'm up for a free demo!
They're both RTS games with a medieval setting. You field a lot of the same units like archers, crossbowmen, swordsmen, knights, etc. What the main differences are is that the wall mechanics are much more involved in Stronghold. Whereas your "castle" in AoE4 consists of a keep surrounded by stone walls, or maybe a landmark surrounded by stone walls, a castle in Stronghold is much more complex. You can layer walls, add crenulations, towers, stairs, and more. You can even mount siege weapons on large stone towers. You can instruct engineers to boil oil and pour it over the castle walls. You can have your troops dig a moat around your castle to stop invaders, and you can place oily pitch on the ground, and light it on fire to burn intruders. If you get really nuts, you can design kill zones within your castle, and I find that to be very fun.
The other main difference from AoE is that you have to manage the citizens of your castle as well as the military in order to maintain your supply chain and economy. You harvest wood and stone to construct your buildings and castle. You hunt deer, make cheese, or grow wheat and apples to provide food. You create weapon smiths to create the weapons required to defend and attack. You also have buildings like a tavern, chapel, and decorations that manage the happiness of your citizens.
It's a free demo and only 3 GBs, so why not give it a shot. This is one of my favorite games from that era and I'm happy that they're remaking it.