Cities are the foundation of any civilization. In fact, the world civilization comes from the word "civilopedia" which was an ancient text tradition of storing information about cities, which has since split into the worlds "city" and "wikipedia".
Civ V uses the next generation of city management interface, and in this case, the next generation is really fucking stupid. Kids these days... In Civ IV it is easy to queue up production; just shift-click the next thing you want in line. Civ V added the ever so slightly useful ability to rearrange the queue items, but did it by shifting the queue to a different menu, so for 99% of use, it is less convenient by a lot. In Civ IV I would regularly queue up units and buildings, no longer in Civ V. To top off the bad production management system, in Civ IV if a producton item has any progress, clicking another item will put the new item at the front of an automatically-created queue, so that a temporary shift in production is a one-click affair, such as if you find yourself needing a jail for anti-war protestors while building a bank. At times Civilization is disturbingly realistic.
Population management has been made less convenient as well. To rearrange the tiles being worked you must open a submenu which is usually minimized, a small issue, and perhaps nice to avoid accidentally clicking and screwing up all the tiles. Specialists have been given a pointlessly less convenient interface. It used to be that adding a specialist meant clicking the up or down arrow for the specialist. Now they are manually assigned to specific buildings. Why? I do not know. They don't have any different production. So rather than a simple click, you must instead find the correct building, which is in alphabetical order, so library and research lab aren't right after each other as would be convenient for someone trying to assign more scientists.
On the plus side, conquered cities no longer have zero culture. Culture is now based on the city rather than the civilization, so conquest doesn't result in a bunch of culturally-dead cities which revolt and join a nearby third party at the first possible opportunity.
When you're sick of micromanaging and don't trust the AI to not fuck it up and spam great people points, both games offer ways to indirectly control cities. Civ IV offers the vassal system, in which a foe who has finally realized that he is utterly defeated will capitulate and must then pay tribute and join you in future wars. This has the downside of making everyone else mad, but also more scared, so they capitulate more quickly, thus proving the domino effect and making Nixon not seem so bad after all. Civ V instead uses the puppet system, where you still conquer every damn city, but by puppeting them rather than taking direct control, you can gain the benefit of their science and gold and suffer less unhappiness, but cannot tell them to make anything in particular and they will never make units (or at least I've never seen one).
If I had to choose one or the other, I'd go with the vassal system. It reduced the repetition of conquering city after city of a defeated foe. But I like the puppet idea. Could these be mixed? Puppets seem like a good system for conquered city states. For larger territories, looks ridiculous to have half the planet consisting of puppet cities. A city here and there makes sense, but at such a larger scale there must be some overall government. For this, vassal states seem like the simple solution: allow large groups of culturally-related cities to be collected into a new civilization which would be a vassal to the larger civilization.
In the area of rapidly building up new cities, Civilization V is far better. Hurrying production in IV required either huge piles of gold or mass murder and neither of those are practical since you can only murder people in the one city. Horribly unrealistic. This meant that starting a new city meant a very long time slowly building up population and buildings. Contrast that with Civ V which has turned gold into a significant mechanic (that's another post right there) and allows you to quickly build up population and production, for a price. With a granary, watermill, and hospital, a city can have a production of 9 food right away, with aqueducts and medical labs speeding up growth indirectly, and there are multiple buildings which add production, all of which mean that a brand new city can quickly get the food and production to build itself.
Looking only at the city management itself, I think Civ IV was superior, since the purchasing of buildings is part of the great change to gold (oops, just spoiled that post).