Not really in the same genre, because most of their games are more "true wargames" but everyone not familiar might want to give Matrix Games site a look.
For a glimpse of how the underlying hex-based system is well-implemented, check out "The Operational Art of War III (TOAWIII). Extremely complex, headache causing opertional-level wargame simulator. Includes about 200 scenarios in which the AI is completely scripted (e.g., Operation Barbarossa; Normandy invasion; etc., etc.) ranging from Napoleonic era to modern (e.g., Arab-Israeli wars). No culture, no techs, no society development, just pure hex-based war game with (drum-roll for this astounding concept . . .) STACKING _LIMITS_ that do not resort to 1UPT! (e.g., 3 brigades can occupy a hex at no penalty, but put a fourth on there and they start to suffer reduced performance, etc.). Certainly not a "competitor" to the Civ series either in genre or in market-exposure, but shows how a well-designed hex-based combat simulation engine works. My guess is those involved in development of Civ5 are probably too stupid to even play and win any of the TOAWIII scenarios on easiest difficulty, muchless understand the underlying dynamics and learn from it.
For a glimpse of very well done international relations integrated in a balanced (and admittedly simplified way) into a game involving international relations: Crown of Glory Emperor's Edition. Best diplomacy engine in the business as far as I know. Again, I suspect the brains behind CoGEE have more capacity in their pinky fingers . . .
For a look at just pure stunning detail, historicity, immersion and challenge at the level of true strategic management: War in the Pacific Admiral's Edition. Again, not really a Civ "competitor," no culture, no city building, no exploration, no techs, in effect, the civilian sector just runs on its own and follows (more-or-less historical patterns). You control the military, down to the level of detail of all squadrons, all battalions, all SHIPS (including auxiliary ships, subs, etc., etc.) individual planes, pilots, weapon-mounts, etc., etc. Not that Civ would be "better" if it strived to be like WiTPAE, but a really gifted Civ development team really could learn some things about how to achieve a sense of realism and immersion from this particular Matrix title.
Distant Worlds: not really my thing, but the 4X space guys seem to love it. Seems to have been a pretty solid commercial success too.
Hired Guns Jagged Edge: sadly, one of those games by a Russian developer that is amazing, and has tremendous potential for expansions, mods, and spinoffs, but then the developer just evaporated. Basically a turn-based tactical squad-level combat game in which you portray a mercernary operating in a fanciful African country "Diamond Coast." I realize that real-time tactical players tend to balk at the turn-based aspect of this one, but honestly I think there is no other way for a game to explore the subtleties of squad-level tactics in any other way. One of my favorite games of all time, and I really wish more like it woudl be made.
Forge of Freedom: similar (same?) engine as CoGEE but instead of Napoleonic Europe covers Am Civ War.
