Civilization IV has done away with separate attack and defend values for each unit in favor of a single power rating. While that simplifies the combat system a bit, there are plenty of other specializations that come into play that add a lot of variety to the system. Spearman, for instance, gain a substantial bonus against mounted units. Archers gain bonuses when defending hills or cities. Archers also get the First Strike power, giving them a chance to take out enemy units before they take any damage themselves. Mounted units typically have a chance to withdraw from combats if they find themselves on the losing end of the combat.
Each unit that wins a fight earns experience points that can be used to buy promotions. These run the gamut from simple power bonuses against certain types of units, or in certain types of terrain, to more sophisticated bonuses like the ability to heal nearby units or perform amphibious attacks. This system not only encourages greater specialization of your units but also makes you feel more invested in them. Believe me, you'll think twice before you send your amphibious assaulting cavalry who have a 25% bonus against melee units against an enemy's island stronghold. Still, they're the best unit for the job, so...
One of the consequences of this system of unit promotion is that it makes it harder to take cities with a handful of units. Each failed attack just gives the defenders more experience points to spend on promotions. In a strange way, the longer it takes you to capture a city, the harder it can become. The game offers up a few ways to work around this problem, however. First, the experience system rewards attackers more than defenders, so holding off an enemy won't earn you as many promotions as taking the offensive will. Artillery will also help out, not by damaging the defenders inside a city (which it can't do) but by diminishing a city's defense bonus.
Artillery can damage units outside of cities however, and, depending on the right promotions, can even hurt enemies in adjacent squares. The cool thing about catapults this time around is that they attack every single unit in a stack. This discourages players from simply putting all their units right on top of one another and maneuvering en masse. Since artillery can be so devastating to grouped units, you'll find that it makes more sense to spread your forces out.