Better than the first one
The first Civilization was already a great game. The second is better in part because of a detectable upgrade in sound and graphics. More importantly, the game is richer as you have more units, technology, wonders, etc to play around with. Also, the introduction of damage bars (as opposed to an all or nothing combat resolution system) goes a long way in alleviating any residual fears from Civ I where you have found yourself exclaiming in surprise, "That cheezy phalanx sunk my BATTLESHIP!!!"
So relax, don't have your battleships run away from those spear throwing punks.
Some of the same problems as the first. The AI didn't seemed to have improved. With more unit wonders and unit types, it is now easier to beat the game. Consequently, the Emporer level in Civ I is harder than the Deity level in Civ II. So if you are looking for a greater strategic challenge from Civ II, it will disappoint.
The Bottom Line
Best game of the genre I've ever played...I never quite appreciated Fundamentalism to its full extent until Civ II.