Advantages of Each
The advantage with seperate attack/defense values is that the user/gamer/player has a quick and dirty way to determine if attacking or defending is the best way to go. However they are determined (and I don't know enough to discuss the nuts and bolts of that!) those values are easy to grasp and manipulate.
The advantage of the single strength value, modified by whom is attacking whom, is that it can give more realistic combat results between units of different types (melee, archery, mounted, etc), where one has an advantage over the other. Pikes defend better against Knights than Longbows, for instance.
The Biggest Difference
The tricky part with the single strength value for the user/gamer/player (not the programmer) is keeping track of what modifies it.
In the C3C world, all that modified the values was the terrain, so it was very easy for the gamer to look at the map, see the units and tell if an attack was a good idea or a bad one, just based on the units and terrain. Terrain times Defense compared to Attack; pretty simple. (As players, things like unit health and leader fishing also figured into the equation, but they didn't change the basic odds.)
In Civ4, the equation got more complex, since it became Terrain times Strength times Unit Type Value/Bonus (of the Defender) compared to Strength times Unit Type Value/Bonus (of the Attacker). Adding in the various promotions of each unit also made things muddled and confused for the gamer, since more math was involved in order to calculate the odds.
My Bottom Line
I think that the system in Civ4 is more accurate, but also more "magical'/black box-ish, since the math is somewhat involved, and that fact (the involved math) makes it seem more complicated than it really is.
I think that the system in Civ3 is easier to use.