I felt religion, in Civ IV, was little more than an excuse for Spain to declare war on everyone. I much prefer the control, power, and diplomacy of the new version, and the method of gaining religion...not even comparable, Civ V wins that hands down.
I do agree with civics. I think the policy trees have a place along side civics, not in place of them, but given the choice, I prefer to have culture give me bonuses though time rather than science allow me to use new forms of government, making it even more powerful (and, in fact, if civics were to be introduced, I'd tie them to science, culture, faith, wonders, etc. rather than JUST science.)
I also like that technology trading is gone in the form from the past, but I'd like to see more of an effect toward science that other civs have, passive or active, but right now, it's pretty minor.
However, in the end, this power and choice thing needed to be changed. In Civ IV, I know I could spend several minutes per turn sometimes micromanaging every little part of my empire. Now, I rarely look at my city screens more than once every several turns. Before, there was more power and choice, but it was sometimes reduced to a chore, and I think it was a better choice to remove too much that could be re-added (and I do hope to see the return of civics in the next expansion, to work along side SP's, for instance) rather than leave too much and the game be unfun due to the amount of time and effort needed.
Well I'm not saying I want religion to be like it was in Civ IV. I actually prefer the customizable belief system in G&K. It's a much more tailorable system and on paper should make me feel more powerful and influential over my gameplay experience than I was in Civ IV. The problem is that I don't feel that way. Religion feels like it has very little influence on other civilizations' relations with and attitudes toward me (other than the fact that spreading a religion to their cities makes them angry.)
That's a design philosophy decision I suspect was made early on, because it runs throughout most systems in the game. Culture, religion, and government type are more about benefits to your own civilization than about influencing other civs this time around. Which is fine if that's the goal, but it's not what I would prefer personally as the player. I want to feel like I'm exerting influence and having an effect beyond my borders with something other than my military. That sense feels drastically reduced to me in Civ V.
With civics, as with religion, I'm not even necessarily saying I want them back. Just that I want policies to have more influence beyond my own civ than they do at present. It would be nice if, for instance, the game could calculate a "governance state" (with a name that you could transparently see, like 'benevolent socialist' for instance) and then generate attitudes toward you based on what other civs' governance states are.
Tech trading, I do really miss. Severely. I like to play a totally peaceful game sometimes from start to finish. And I liked sort of roleplaying that I would share techs with everyone so that the world could unite and be on an equal footing. That may not sound particularly appealing, but the point is that in Civ IV there was the freedom to cater to that play style without compromising the game for anyone else. Whereas in Civ V, that's all but impossible now. At least in my experience. Not to mention, when playing a team against the AI (something I loved doing with friends) it was nice to share techs and feel like an alliance.
As for micromanagement, I actually feel there's more micromanagement now. Civ IV let me automate virtually everything, and everything could be done seamlessly and intuitively. To me Civ V feels much more opaque and unintuitive, and requires a lot more attention to things like buying tiles and constantly dealing with contacts from city states and so forth.
But that's me.