In Civ V, you've got to choose where you place units carefully, and you have to pay close attention to where enemy units are. In my most recent game, I went to war with the Japanese and we had only a three-tile border, so I had to move my large army through a narrow bottle-neck while also contending with Japanese counter attacks. It was the most satisfying conflict I ever had in a Civ game because my decisions about where I placed my units made a huge difference to the war, which isn't something that I felt was true of Civ IV.
I had a bit of the opposite experience yesterday that also demonstrates how much better the combat is. I was trying to take an English city that was past a choke point, made even more difficult by a mountain I had to maneuver around. It was during the medieval period so the English had Longbowmen instead of crossbows... which aside from being a big stronger, also have a range of 3 instead of the standard 2. Given the location this gave the English a huge
tactical advantage that I wasn't prepared for so despite my superior numbers and slightly superior technology I was simply unable to take the city. I couldn't get units in fast and in large enough number to get passed their ranged defenses. Because of my poor planning and the terrain I had no choice but to pull out of that war.
In Civ IV, I just would have had to build a massive stack and move it in. No tactics, no planning beyond building enough units. It would have been much easier to take the city, but also much less interesting and certainly less complex.
Incidentally, I played that whole game from start to finish without stopping for a time of about 7 hours. I think I need to give Civ 5 a rest for a few days for my sanity's sake