The more I play this game, the more I enjoy the blending of the two "games" in the game. It combines a decent Civilization-type management game (minus the gigantic tech-tree that I, personally, can do without) and a simple RTS battle system into an entertaining package. My only real complaint is that the system is too simple, but it is from 1996, so you have to let some things slide.
I haven't found too many other games like this. I have Civ 4, but the combat system is really non-existent. I also have Star Wars: Empire at War, which is the closest I've found to this... but I can't get into it.
"I have an idea. It starts with 's' and ends with 'litting their throats.'" ~Belkar from The Order of the Stick
since this game is more tbs than rts, I think a good way to kind of move out of Lords of the Realm is playing Stronghold, it's kind of the Age of Empires version of Lords of the Realm, but it's still freaking awesome because it brings pretty much all of the economics of Lords of the Realm into it, you need wood and the proper resources to make weapons, but you need to make workshops specifically for making those weapons, you need to balance your popularity but you can't be too lenient or they get lazy and if you're too tyrannical they don't like you, you have to be careful with tactics. You have to do all that and more all in real time.
I don't know if that applies to all of the Stronghold games, but it applies to the Crusader one that I have. It's a good game and I liked it as the more RTS type of Lords of the Realm :)