Interesting comparison - but I'm afraid many people will stop reading at this: "If anything, diplomacy is a draw, with neither game being definitively more deep than the other."
"Finally, you cant trade maps or technologies in Civ 5. Does that make it less complex? I suppose in some slight way, but it does serve to keep all the different civilizations from instantly catching up to each other in the middle ages, making for a more varied game experience."
I'd argue that CIV V's system of Research Agreements work in the opposite manner - where it allows those already ahead to stay ahead. Both mechanics have their flaws.
As far as Civics and Policies go, it's generally a matter of personal preference. I don't think one could be considered more complex than the other. One thing I did like about Civics was that they were tied to Government types that were unlocked through the Tech Tree. This added a layer of depth to the Tech Tree itself in regards to what paths you would choose to take. This also meant that you wouldn't always have the exact same Civics become available in the exact same order in every game, as is currently the case with Policies being unlocked by Era's. (Having less policy prereqs could go a long ways towards limiting this).
But again, this is just personal preference on my part. If Social Policies had any sort of drawback instead of constant bonuses, then I'd lean towards them being more complex.
"This is a clear example, in my mind, of complexity for complexity's sake. I'm not sure how dividing up the different meters, not just between production and growth, but also between each city, helped make the game any more deep."
I think mechanics like health and local Happiness offered more in the sense of immersion rather than subjective complexity. One could argue that it takes more micro-management to constantly keep tabs on global happiness in situations where the AI hands you 5 cities after a war, or if you happen to lose a city with 3-4 luxury resources and all of a sudden you're down -20 Happiness.
On the other hand, Health and local Happiness allowed each of your cities to feel unique from one another whereas in CIV V, each city more or less feels identical to the next, (although this has improved with patches). I think the overhaul Firaxis introduced regarding starting locations, (how Russia would start next to tundra for example), was their way of bringing back this sense of immersion from individual cities.
"One small caveat: There is a big difference between design and execution. Many may be thinking He didnt even talk about AI! This is because AI and how good it is at playing the game against you is all about execution. Civ 5′s AI in not even close to on-par with where Civ 4′s AI ended up being by the last patch. This difference does not address design complexity though. It may make the AI a more fun opponent in Civ 4, but more fun does not equal complex."
An interesting comparison here would be to relate the design of military units and war to Civics and Social Policies. Civics provided positives and negatives, and the order in which you chose to use them varied from game to game, (based on your Tech path, for example). This is similar to how Military Units work in CIV V. Different units with different positives and negatives, and how you position them affects the overall outcome. Conversely, Social Policies almost feel like stacks of doom. There are no negatives to having more of them, more is better in fact, and having the most of them can actually lead to a win in the game.
"Totaling the score, we have Civ 5 with deeper combat, Civ 4 with deeper happiness, and a draw across the rest of the board. That, essentially, denotes a tie (and if you had to pick between Civ 5′s war and Civ 4′s happiness, I think we all know what everyone will pick)."
I don't think the answer to this will be all that lopsided as long as the AI and Dipomacy remain in their current exploitable state.
Overall I'd have to say that CIV V doesn't come close in terms of complexity to CIV IV, but again that's just personal preference - and in most cases this just boils down to whether or not you prefer the building side of Civilization, or the warring side.
All in all a good read. Nice job.