I really don't know why I'm bothering with this. I mean, I do, because I'm procrastinating from work, but still.
Firstly, Civ3 had Cultural borders as do later Civs, what makes Civ4's Cultural Border system 'the mos complex'/'best'?
Points to debate: Civ4's Cultural Borders reduced complexity, just as Civ 3's did, because 1) you didn't have to think about city placement so carefully and could dump a city anywhere in the right general vicinity of decent tiles. 2) Cultural flips made war options less complex as the strategy of just shrinking a neighbour down a bit has vanished from the game, you now have to either raze or take the entire Civ AI out lest your taken city simply flips back to it's previous owner. 3) Civ 2 had Civil Wars whereby capturing a rival Capital instigated a Civil War which split their empire (or yours) in two, providing a lot more options when deciding on how to effect a civilisation's borders. 4) Cultural borders are not an option involving choices, they are something that happens automatically and it's stupid if you don't invest something into its production.
Civ 4's cultural borders are unique in the sense that they allow you to wage "cultural warfare," sniping tiles or even cities without having to fight over them. Whether it's because they're stronger than you, they've got a Defensive Pact with someone scary, you're tied up in wars on other fronts, or you just want one or two tiles but not badly enough to fight over them. With regards to 1, you still absolutely had to think about city placement, in fact possibly even moreso than in earlier installments, because your BFC wasn't immediately accessible. Until your borders popped, you could only work the eight tiles adjacent to you - and unless you're a Creative leader, it's probably going to be quite a while before those borders do pop. One of the most agonizing decisions about city placement in Civ 4 is whether it's worth moving away from a truly awesome BFC to get a pretty strong initial 8 tiles. I do actually partially agree with your second point: It can be frustrating to be forced to eliminate or almost eliminate another civ when all you wanted was one or two cities but their remaining cities exert such strong cultural influence that unless you've got a Great Artist to bomb with somewhere nearby, you won't be able to work any tiles (this is also why, perhaps somewhat counterintuitively, Creative is generally a better leader trait for warmongering than anything else). Civil Wars were done away with for a reason in Civ 3, and that's because as much as they're a cool concept, they ended up being more problematic than anything else. First, because if a player says, for example, "I want three opponents in this game," it's usually for a reason and they aren't massively enthused about having that number suddenly increase, and second because the AI simply didn't get the importance of preventing Civil war and so it became a magical "loliwin" button against them.
Your fourth point makes me question whether you've even played Civ 4. The amount of choices you have for cultural borders is pretty significant. Producing certain buildings, choosing certain leaders, running the right specialists, choosing certain civics, and debating whether to devote commerce to it are all major parts of expanding your cultural borders.
When have tile improvements not mattered? Are you even going to list any that are unique to 4 and somehow represent something meaningful to your argument?
Civ 4 was more complex in two ways: First, it implemented a food/commerce dichotomy. Now instead of roads giving commerce and being able to combine them with irrigation, you've got to choose between farms or cottages. This was a massive change, and actually resulted in one of the more interesting aspects of Civ 4: The choice between a Cottage Economy, Specialist Economy, or a Hybrid economy. The advent of Great Person Points meant that a city running a lot of Specialists was a far more viable strategy than it was in earlier Civs.
Second, it implemented more specialized tile improvements: Workshops, Watermills, Lumbermills, and Windmills. A sort of rite of passage for Civ 4 players is the moment when they begin to recognize when they should begin to replace Mines with Windmills, or how to structure a Workshop economy. Civ 4's worker game slowly reveals more of itself to you the more you become familiar with the game, and there's a degree of decision-making there that no other Civ has matched.
It also introduced major resource bonuses, which I liked.
the great persons
All of them? You mean like Great Artists and Great Philosophers? I remember being really quite underwhelmed when the partially non-controlable RNG gave me a shitty leader instead of the one I wanted. However, in Civ 3 Great Leaders are always great, because you can always use them to build a Great Wonder or an Army/Small Wonder. However, it's a bit shit in Civ3 that one of their uses, Scientific progress, simply doesn't work. A bug that no-one ever bothered to fix. Also in Civ 3 they only spawned from RNG in the first place, so they were even less controllable by player skill. It's not a complexity in Civ 4, it's just a bonus that pops up every now and then which, again, you'd have to be pretty dumb to not take notice of and let it do it's thing without much human involvement. At least in Civ 3 playing to generate Great Leaders is a genuinely alternative game path that can be specialised towards with complex knowledge and skills. You don't seem to want to mention why Civ4's leaders are supposedly so much more complex than any other game's...
There were no Great Philosophers in Civ 4. You've actually got a pretty idiosyncratic view of Civ 3 leaders - at least over at CivFanatics, leaders were generally regarded as one of the worst parts of the game, and Scientific Leaders are specifically one of the main reasons why there's a substantial part of the Civ 3 fanbase that maintains that Conquests made the game worse. Randomly generating a leader that could auto-build a Wonder was just wayyy too chaotic and frustrating. Civ 4 completely fixed the leader system. The RNG is entirely controllable, and I don't know why you'd think otherwise. The potential Great People a city can generated is determined 100% by player input - specifically, which specialists you choose to run and which wonders you choose to build. Again, this is one of the things that gave more choice to the game: "I'm running mostly scientists in this city, because I'm hoping to generate a Great Scientist, but I really need more production than what my tiles can give me. Running a Priest or two would beef that up, but then I'm at risk of polluting my Great Person Points with a Great Prophet that I don't need right now."
It is true that a weakness of Civ 4 is that not all Great People are created equal: Great Scientists are by far the best for the first half of the game, and then Great Merchants are by far the best for the second half of the game, and Great Engineers are second best for the whole game. Great Prophets are extremely powerful but you'll probably never need more than one or two, and Great Artists and Great Spies are generally mostly useful for specific styles of play. Absolutely indispensible if you need them, but Golden Age fodder otherwise.
Great People in Civ 4 are what makes running a Specialist economy viable, and being able to micro your cities and workers to get just the right amount of GPP in the right category to generate the right great person at the right time is a pretty popular style of play. The degree to which you can make Great People an alternative game path in Civ 4 is greater than the degree to which you can do so in Civ 3, and frankly, less game-breaking as well.
What makes Civ 4's unit promotions any better than any other Civ game? My experience was that as soon as my Warrior got quite experienced the Tech-tree had moved on to the point where I needed to replace the unit with a better unit anyway. Also, because the game uses the same SHIT RNG that Civ 3 uses then Promotions don't necessarily mean shit anyway, you could still roll a 1 no matter how good they were... and the small percentage benefit is barely worth the effort of playing towards it and delaying your attacks to always get the improved unit at the front line, fully healed. It's just another bonus that happens and you say, cool, and move on without taking much notice of it. In Civ 3 acquiring Unit promotions can be a specific alternative option to battles where wasting a few turns healing and getting the guy to the front again can provide serious long-term benefits as only Elite Units can produce Great Military Generals. If Civ 4 fully promoted Units can do something amazing that I'm not aware of, please let me know.
Again, this makes me wonder if you played Civ 4 for more than one or two games. The unit promotion system is dramatic and allows you to custom-tailor armies to certain situations. They weren't a "small percentage benefit," they were a drastic change that could allow units to take on different situations. Getting a unit to Medic III ASAP is, like, an essential part of any military campaign. The ability to speed up healing of everyone around you simply cannot be matched. A few City Raider promotions can make units extremely effective against cities, and of course, you can't sneeze at the massive power of siege with upgraded collateral damage. Also, a lot of the experience for promotions in Civ 4 is going to come from outside of combat - specifically, your Civic choices. If a city has a Barracks, then running Vassalage and Theocracy allows every unit built there to choose two promotions - three, if your leader is Charismatic. This lets you customize your army right out the gates. Of course, there are other powerful options for Civics in both of those fields as well, so it becomes a very difficult choice (moreso in the Religious tree - Vassalage is probably the weakest choice in the Legal tree).
High-tier promotions are also extremely powerful. You've got Blitz, which allows Mounted units (and tanks, of course) to attack multiple times in one turn without penalty; Drill IV, which gives you 3 guaranteed first strikes and 3 chances for a first strike, making it very possible for you to wipe out an enemy without taking damage; Commando, which lets you use enemy roads (something that happened by default in earlier games, sure, but in a game where you can't do it, the ability to do it becomes very powerful), and, of course, the investment-heavy Combat VI, conferring +75% strength and a bonus to healing.
The end result is that properly promoted units can often end up taking down even units from the next era (uh, depending. There can be huge gaps sometimes. Well-upgraded Pikemen taking down Cavalry is one thing, but don't expect well-upgraded Frigates to bring down Destroyers).
Civ 4's Promotions system is, effectively, an attempt to import SMAC's unit customization into a Civ environment. While it's obviously nowhere near as good as SMAC's workshop, it's still a massive step up from earlier Civs.
The long and short of it is that Civ 4 introduces a massive amount of new mechanics, most of which add a lot to the game's complexity. I haven't even touched on many of them - health, additional commerce sliders, religion, etc. Health in particular is a huge one - again, the type of thing that seems pointless or minor when you first play, but that can have a dramatic impact the more familiar you are with the game. Especially when it comes time to industrialize.
