I was hugely disappointed by Civ 4.
Areas where Civ 3 is better:
Diplomacy
I will agree that diplomacy has been significantly weakened. Although the variety of diplomatic options has increased, the flexibility in how you can use them and a lot of the fierce diplomacy of III is gone. I just don't think it was very well-implemented. Streamlined in this case meant simplified. I DO, however, like the fact that you can influence the AI against other AIs.
Military
Overall waging war was much more fun, more interesting, and overall more satisfying in III. They tried to do too much with the combat system; the promotions are a good idea, but there's just TOO MANY of them! Also, as noted before, the bombardment system makes absolutely no sense at all. I also don't like how you have to have super huge mega-armies to make any progress. The rock-paper-scissors mechanic just feels a little forced. A lot of the fun in waging combat just seems to have been lost. Drawn-out wars of attrition with neighbors are more of a drag than they were in III, when they could still be fun.
Expansion and the maps
There's many problems here.
No more sense of "creating" an empire. The small maps means that maps are filled up quickly. Because there's so much useful terrain and so many different resources, there's hardly a bad place to place a city. Cities create larger footprints, the decision-making process in placing cities is almost eliminated, and simply a lot of that "empire-building" feel has been lost. My favorite part of Civ III is when you're expanding and carving out your own niche in the world, struggling to survive and vigorously competing with neighboring civs. It just doesn't feel "Civ-like" in IV. The crippling handicap on creating large empires doesn't help much either.
And about the maps themselves; besides the seeming elimination of useless terrain and their small size, they're just so unrealistic and uninteresting. They never form mountain chains, the shapes and geographic features are uninteresting at best, and the patchwork distribution of terrain is totally unrealistic. However, it is nice that there's "tundra hills", "forest hills", "desert hills", etc. It rectified one of my few complaints about the maps in Civ III.
Artificial intelligence
In some areas it is an improvement. They're shrewder diplomats and ultimately at least a little bit smarter in combat. However, for being released 4 years after III the AI doesn't take nearly enough of a leap. My biggest problem is that they aren't nearly aggressive enough, especially towards each other. One of the coolest things about Civ III was watching the AI civs war with each other, something that I never really experienced to any significant extent in Civ IV. I've heard that Beyond the Sword improved the AI considerably, however, but I was never interested enough in buying it to find out.
Faster workers, slower game
My workers would quite often have even less to do than in III. Despite the increased worker options, they worked faster and wouldn't have to take an extra move after moving into an unimproved tile to build something there. This means that more could be done with less, but because of smaller maps and faster work times, they stood around a lot more. Left long stretches of the game with literally nothing to do. The less interesting diplomacy, more difficult combat, and lack of AI-on-AI action, overall it felt a lot slower to me.
The graphics
As mentioned before, the graphics are just too cluttered and flashy. However, this is a relatively minor complaint.
More focus on cities, but cities aren't any better
What I mean by this is that, despite the fact that each city takes on much greater importance, if anything they can't do quite as much as they do in Civ III. It would've been nice if they would've fleshed out city management some more so as to make city management more important. I believe this is important because of the increased focus on cities; you have less cities, and ultimately about as much to DO with them as you did in III. See where I'm coming from?
They went overboard with culture
No explanation really needed. Culture is way too powerful for its own good. It should be a mostly passive element that can be dinked around with and improved like in III, but it shouldn't become the forefront gameplay element.
Things about Civ IV that don't quite work:
Religion
The idea of having religion in there is a good idea, but it seems like it was just tacked on. First off, the idea that you can "see" into cities with the same religion is ridiculous. Also, I hate how once a religion becomes established in a city, it's stuck there forever. Religions don't "overpower" other religions naturally; they'll only spread to cities that don't have religions. You can't wage a holy war and purge certain religions from your city, etc. This makes it extremely difficult both for later religions to take hold and for there to be any real change in the status quo of religion throughout the game. However, the cultural, financial, and diplomatic aspect of religion is good.
Technology tree
I love the increased accuracy, increased importance of each technology, and the different paths to each technology. I think that's a great idea. However, does it ever seem just TOO open to anybody else?
Economic system
Well, I know it's improved. It's just that nobody knows that because you can't tell what the hell is going on with it. Also, advisors are also bloody useless, although the fact that you can see all of the other civs on the foreign advisor screen is a HUGE benefit.
Leaders instead of civs
Well, I like that there's different leaders...I'm just not too fond of the fact that leaders essentially replace civs.
Things I like about Civ IV:
Great people
I love great people. They're easily the best new feature in the game.
Resource system
I like the variety of resources and the bonuses of each. No more separate "bonus, luxury, and strategic" resources. All can be traded, all can be improved, all provide a variety of different benefits, etc.
Vassal States
Awesome. It really should've been in Civ III. That's all I have to say.
Worker options
I do like how there's so many different and useful things that workers can do. Mines are more restricted, which is much more realistic, there's cottages, which are a nice touch, and every resource can be improved in some way. Again, though, they never should've made workers work as fast as they did, and they never should've given them an extra movement point.
Civics
Not a flawless idea, but I like the flexibility that comes with choosing different government traits. It could've done with a little more control, though, such as a combination of the governments in Civ III with different government traits in Civ IV.
No corruption, no city rioting
Although yes, it is replaced with the annoying empire-killing handicap, the fact that corruption itself is gone is one of the few things where I can honestly say "thank god for CIV IV." But one of the VERY few.
It's the same with city riots. Luckily, they won't fall into civil disorder; discontented citizens just won't work. It makes it much easier to manage a city and ultimately less annoying. Civil disorder was just bad in Civ III.
Overall, it comes down to this:
Civ IV sacrificed DEPTH for BREADTH. It does LESS with MORE. It's just so much more simplified and, ultimately, slow to me.