Played two singleplayer games, one on the easiest (Chieftain), one on the second. Won both, but I don't think my opinion would be different if I would have lost it. Also, note that I don't have Xbox Live Gold, so this all comes from SP experiences. I know two games offline probably aren't enough for a well-rounded opinion on the game, but here goes.
I have been playing Civ4+warlords+beyond the sword a lot with my brother the last week and I can't help but feel disappointed with this game. Civ:R is in every sense of the word a step back from Civ4 and even Civ3. Civ4, for me, is all about depth. About the leader traits, the worker management, the citybuilding and warmongering and expanding aspect. Everything in the PC Civ games basically got dumbed down in Civ:R. There are no more workers, the leader traits are there but since they change depending on what era you're in you can't really have a long-term strategy based on the traits since it can change so quickly. Citybuilding also got dumbed down, I didn't really notice any sick or healthy, happy or unhappy people in any of my cities. Tile management is there, but since there are no workers you can't dedicate cities to production or food or culture. I also don't like the warmongering much. Artillery like the catapult is not needed anymore to destroy enemy fortifications in a city under siege. Eventually boils down to combining your cossacks or whatever your unique unit is into armies and getting on a happy spree. Nothing like a Lightning Ninja Cossack Army attacking and conquering city after city, but boy does it get old fast. After finishing two games, I feel like I've seen 95% of what the game has to offer me. The wonders are not very unique or game-changing, same goes for civics or the tech tree.
Civ4 is probably too complex and difficult for most gamers, pc-gamers and console-gamers alike, but if Civ on the console means that all the depth goes straight out of the window at the expense of quirky looking advisors and barbarians jumping out of bushes yelling at the player, I'm out.
My brother, the other civ-player in my house, likes the game though. Not as much as Civ4, but he likes it as a quick, funny Civ-game played in short periods of time when we don't have time for 5 hour Civ games over lan. And maybe I should view Civ:R this way, but I view the X360 as a equal system as my PC and I view games on both systems the same way.