The OCC provides a great challenge on Noble and above. Consider the fact that rival civs will continue to trade techs around you -- while you might have a large tech advantage, it may erode quickly as the game progresses. This is because later techs take longer to research, and you still only have one city to provide research. Then, when the AI trades with another civ (or a few other civs) for tech, you can easily fall behind.
You only have one production centre, while other civs have multiple cities, which can be simultaneously building wonders, units and buildings. In other words, while you can only produce something to improve your civ one thing at a time, all the AI players are capable of making multiple improvements in a single turn.
While it is quite easy to build up a large army to keep enemies at bay, a war on multiple fronts can be quite costly. But Conquest is possible. Domination might be, if one were to play on a tiny/duel-sized map, though I haven't tried. Going for Time/top score can be difficult; chances are that with multiple cities and a larger population, at leat one other civ will be ahead of you in score. While your one city will eventually be of legendary status, you can't go for a Cultural victory because you'll never have three cities of legendary status. Spacerace provides a tough challenge, as a close tech race means that your rivals will be producing spaceship parts at the same time, and again they have more production centres. As for Diplomatic victory, also possible, but those early friendly relations are key.
In the CivIV OCC, the limit of 2 national wonders per city is gone, which is nice. This means that your city can, at the same time, be an excellent GP farm, a major production centre, and a sceintific powerhouse. But in order to get it to that point, you have to manage carefully your resources, and pay particular attention to improvements in your fat cross, ensuring that you have a good mix of food, commerce, and hammers available for your city.
In my opinion, the OCC offers the player a well-balanced option, as you really have to pay attention to all of the aspects which make Civ a great strategy game -- micromanaging, military/warmongering, building, along with religion and diplomatic relations. In the OCC, ignoring any one of these can cost you.