When researching they've added links and useful synopses of what a particular tech or goal will achieve, which was another great idea. They've retained some of the better ideas like the Public Works concept, which allocated a percentage of taxes toward specific city improvements like farms and roads, thus freeing settlers to do what they do best, found cities. Likewise the Trade model is intact and still works elegantly, with a nice graphical flourish. Again, your empire supports troops, not specific cities, which was another good concept and you can easily stack troops into armies rather than move individual units around the map.
They've also improved the Diplomatic model simply by adding a lot more choices. If you don't like an offer on the table you can reject it or alter it. You still choose from a wide variety of stances to make your point plain only now you can add a specific threat. "Give me that tech or we go to war," removes the ambiguity when you'd refuse a power with good reason and then suddenly find yourself in a war you didn't want. But this is largely one-sided. You may make your proposals interesting but its disappointing the answer you get is a static and unyielding "Your proposal has been rejected." Look at Alpha Centauri with its well-defined leaders and the characteristic way they had of negotiating. It added a great deal of depth to the negotiation and therefore to the game, so it's notable to remark that all of that is absent here. It's like negotiating with a computer precisely because that's all you are doing.
The warfare component still allows you to stack up to twelve units into more mobile combined-arms armies and this makes the war easier to wage. This seems like a good concept at first glance because, gone are the days when you could lose a stack of troops in one encounter because the first unit in the stack lost the fight. But it creates a lot of problems too. Combat automatically places melee troops in the front line, missile troops in the rear and the new flanker units on the sides but you can't decided who fights first. It's possible to watch your army win but lose all its most valuable troops. Further, CTP2 retains Civ's penalty where the defender of a city loses a population point for each battle lost. In Civ2 this meant a protracted battle could reduce a 10-point metropolis to a 2-point ghost town. An unhappy and unproductive prize to be sure. Here one army can defeat the city at a cost of 1 population point, making the task of rolling over an empire all the easier.
They've also kept the controversial "unconventional" warfare units, like the Slaver, Priest, Lawyer, Televangelist etc., with the addition that any unconventional unit can see all the others. This makes it much easier to spot, eradicate or counter them effectively (before only the same units could see each other so you were faced with creating Slavers so you could spot enemy Slavers). But these units are still unbalancing, annoying and frankly they hurt the suspension of disbelief the game tries to evoke.