Olleus
Deity
There are an awful lot of people on this forum scream heresy about how much CiV has been dumbed down for the console market and how it is a much simpler shallower game, or that it is merely a war game. I'll look into 5 key examples to see how this is the case.
Economy
Civ4 was the first civ game where you had to worry about how much commerce you were generating - before all it involved was plonking down roads everywhere. In Civ4 you have to build cottages/have specialists and worry somewhat about trade routes - especially international ones in the mid-late game. However, in 99% of cases the use for gold was easy, to allow you to run the science slider as high possible. There was no other real use for it. In 5 the choice for the economy is very different. For a start you have to chose between science or gold (or culture) from the very start. For science you run your population as high as possible, so you build farms; for gold simply build trade posts. But its more complicated than that, because high populations lead to more gold from trade routes, and more gold leads to more research agreements.
In short, there is more variety in 4 from how you generate commerce; but in 5 there are far more uses for it which require careful thought.
Culture
Culture in Civ4 was rather dull. Once a city had expanded its big fat cross, there was little importance for it in most circumstance. Sometimes you'd want to start a culture battle with another civ to win or lose a handful of tiles or to get a resource 3 tiles away, but that was the exception not the rule. In Civ5 with the addition of Social Policies, its completely different. While early SPs are very good, the late game ones are incredibly powerful. Culture is now genuinely useful at every stage. Even later on in the game I care about the cultural output of my core cities. This was never the case in Civ4 (bar cultural victory of course). This is clearly not one area which has been dumbed down.
Warfare
Tensions run high around here about 1UPT, but the bottom line is, whether you like it or not, that removing SOD make the game more complex (not saying anything about its realism). Having to chose which units go where as well as having ranged bombardment adds depth to the game. This is obviously one area where it hasn't been 'dumbed down'.
Diplomacy
With all its figures on show and Religion in the game, civ4 diplomacy was almost perfectly transparent and quite easy to understand and manipulate. Civ5 (post patch) feels like the leaders are following the rules of real politik and although alliances can be made; don't expect anyone to act directly against their own best interests. I'm not sure you can say if either system is simpler than the other, it just depends on how Machiavellian you want your game to be.
Corporations/City States
I've put these in the same category because they're both about using gold for other stuff. Corporations in Civ4 never seemed to be widely appreciated and using them was often banal and repetetive - they could be used as both a weapon and a tool for growth but weren't all that important in either respect. City states on the other hand are also a bit tedious requiring constant gifts of gold but there interplay in diplomacy and quests liven the game up a lot. In this case, the sheer number of interactions with other game systems means that City States are a more complex system than Corporations.
Social Policies vs Civics
Social policies allow a much greater diversification and specialisation that Civics, but aren't refundable and don't allow you to change your mind. Some say that forcing you to plan ahead is more strategic, others that it removes player choice - on the whole its fairly balanced. However, another difference is that Civics were given as freebies as you went along the tech tree, while social policies require an active investment in culture growth. A system that requires you to invest (and hence sacrifice something else) for a later gain must be considered one that increases complexity.
Empire growth
In civ4 the only combatant of ICS and REX was maintenance cost. However, an even slightly matured city would always pay that back easily. Hence, the best tactic in Civ4, usually, was constant slow expansion. In Civ5 the cost of expansion is happiness, and cities generally do not ever provide more happiness that they provide. Hence, there is a real cost to large empires - both in Happiness and increased SP cost. This means that there is a real grand-level strategic decision to be taken about, not just how fast you want to expand, but the total size you want to be. An example of an additional non-repetitive interesting decision - the hallmark of complexity in a strategy game.
Espionage
Little to say here, clearly the Civ4BtS system was far from perfect and wasn't that great; but the total removal of a game mechanic with no replacement what so ever can only really be called dumbing down.
Conclusion or tl;dr
Read the last line from each paragraph and make your mind up
Economy
Civ4 was the first civ game where you had to worry about how much commerce you were generating - before all it involved was plonking down roads everywhere. In Civ4 you have to build cottages/have specialists and worry somewhat about trade routes - especially international ones in the mid-late game. However, in 99% of cases the use for gold was easy, to allow you to run the science slider as high possible. There was no other real use for it. In 5 the choice for the economy is very different. For a start you have to chose between science or gold (or culture) from the very start. For science you run your population as high as possible, so you build farms; for gold simply build trade posts. But its more complicated than that, because high populations lead to more gold from trade routes, and more gold leads to more research agreements.
In short, there is more variety in 4 from how you generate commerce; but in 5 there are far more uses for it which require careful thought.
Culture
Culture in Civ4 was rather dull. Once a city had expanded its big fat cross, there was little importance for it in most circumstance. Sometimes you'd want to start a culture battle with another civ to win or lose a handful of tiles or to get a resource 3 tiles away, but that was the exception not the rule. In Civ5 with the addition of Social Policies, its completely different. While early SPs are very good, the late game ones are incredibly powerful. Culture is now genuinely useful at every stage. Even later on in the game I care about the cultural output of my core cities. This was never the case in Civ4 (bar cultural victory of course). This is clearly not one area which has been dumbed down.
Warfare
Tensions run high around here about 1UPT, but the bottom line is, whether you like it or not, that removing SOD make the game more complex (not saying anything about its realism). Having to chose which units go where as well as having ranged bombardment adds depth to the game. This is obviously one area where it hasn't been 'dumbed down'.
Diplomacy
With all its figures on show and Religion in the game, civ4 diplomacy was almost perfectly transparent and quite easy to understand and manipulate. Civ5 (post patch) feels like the leaders are following the rules of real politik and although alliances can be made; don't expect anyone to act directly against their own best interests. I'm not sure you can say if either system is simpler than the other, it just depends on how Machiavellian you want your game to be.
Corporations/City States
I've put these in the same category because they're both about using gold for other stuff. Corporations in Civ4 never seemed to be widely appreciated and using them was often banal and repetetive - they could be used as both a weapon and a tool for growth but weren't all that important in either respect. City states on the other hand are also a bit tedious requiring constant gifts of gold but there interplay in diplomacy and quests liven the game up a lot. In this case, the sheer number of interactions with other game systems means that City States are a more complex system than Corporations.
Social Policies vs Civics
Social policies allow a much greater diversification and specialisation that Civics, but aren't refundable and don't allow you to change your mind. Some say that forcing you to plan ahead is more strategic, others that it removes player choice - on the whole its fairly balanced. However, another difference is that Civics were given as freebies as you went along the tech tree, while social policies require an active investment in culture growth. A system that requires you to invest (and hence sacrifice something else) for a later gain must be considered one that increases complexity.
Empire growth
In civ4 the only combatant of ICS and REX was maintenance cost. However, an even slightly matured city would always pay that back easily. Hence, the best tactic in Civ4, usually, was constant slow expansion. In Civ5 the cost of expansion is happiness, and cities generally do not ever provide more happiness that they provide. Hence, there is a real cost to large empires - both in Happiness and increased SP cost. This means that there is a real grand-level strategic decision to be taken about, not just how fast you want to expand, but the total size you want to be. An example of an additional non-repetitive interesting decision - the hallmark of complexity in a strategy game.
Espionage
Little to say here, clearly the Civ4BtS system was far from perfect and wasn't that great; but the total removal of a game mechanic with no replacement what so ever can only really be called dumbing down.
Conclusion or tl;dr
Read the last line from each paragraph and make your mind up