My liking of Civ 3 is simple (and just an opinion)
Civ 3 is like a "power-gamer" type of game, since there's a lot to know and practice.
I want action
I want tons of extra details. I want tons of responsibility. Civ 3 delivers.
Civ 4 is just too "watered-down" for me.
Yes there are many aspects of the game in Civ 4, but they're less "action-packed".
"Research religion tech, build missionaries" just isn't as fun as fighting turn-by-turn for survival...
Civ 3 Military:
You are always in a losing position, since AI has large bonuses, huge swarms, tons of cities.
Your military is weak for most of the game.
Brains, tactics, strategy, the kitchen sink are required to win.
Civ 3 Turnsets:
You control every detail of your empire. Great responsiblity = Great power
You control every detail of your hundreds of units. Great responsiblity = Great power
You control every detail of your dozens of cities. Great responsiblity = Great power
Civ 3 Scale:
You're always struggling to manage your military.
You're always struggling to manage your empire.
You're always struggling to win.
Civ 4 Military:
Everything is balanced. Just build the required counter unit / catapult. You win.
Civ 4 Turnset:
There's just not much to do each turn.
Change 1 build, move 5-10 units, Make 1 trade...
Civ 4 Scale:
Less detail / smaller scale means that "action" is harder to find, and doesn't last as long.
Don't get me wrong. There's
tons of great ideas in Civ 4.
They just weren't implemented as well / challenging / fun as they could have been.