Here is an overall objective look at 3 verse 4:
Civ 4 is geared towards:
Macromanagement, developers tried to get rid of all forms of micro, so no nitty gritty down and dirty here.False
Combat uses 1 number, but does have promotions and unit bonus'. So combat is easier to see who is likely going to win based on the single number strength factor, and game shows info on screen as well.
Civ 4 is not EpicSubjective and huge since a large empire often consists of under 10 citiesFalse, this was done to put in 3d graphics. But games will (definitely) not become overwhelming chores as the largest Civ 3 maps often can.
Civ 4's 3d graphics are nothing awe inspiring; when the game came out they were average, and now they could be considered very outdatedSubjective - Graphics? In a 4X?. This is comparing Civ4 to other top-notch games of it's time at release (in which Civilization ranks very high)False - it was only adequate even then. But 3d is inevitable, so I see Civ 4 as being a jump off platform and expect Civ 5 to have good/excellent 3d graphics.
The Developers listened to all complaints of Civ 3, and based Civ 4 off of that by attempting to fix those problems; as well as adding in new features.
Civ 3 is geared towards:
More Micromanagement based, but no micro is needed to play the game, but you won't fair as well as doing some micromanagement of your empire.
Combat uses the Attack and Defense combat values, which I feel is far superior to a 1 number strength valueSubjective - Try giving a reason why Civ3 one unit type stacks are better. But combat does not has specific unit bonus', which I like in Civ 4.
Feels Epic in that you can have half a thousand cities on a map (and more now)... but might feel too Epic at times when you may have too many cities; and many feel overwhelmed even trying to do a little bit of micromanagement with this number. But smaller maps can be selected.
Uses Sprite Isometric graphics which are also outdated, but game is close to a decade old.
Developers listened to things in Civ 3, such as Spearman beats Tank issue, corruption, and complaints against micromanagement, and changed these for the 4th version. Thus Civ 4 is Macromanagement based, corruption is no longer an issue, and units now have single strength value.
I tend to hear most often:
Players don't like Civ 3 due to corruption, micromanagement, combat issues, AI has some issues.
Players don't like Civ 4 due to small empire sizes, so-so 3d graphics, single number for combat, feels slower/loss of interestTheres no reason to think people with complaints about graphics or speed would go back to a worse looking, slower game..
Although this is no exhaustive list.
Civ 4 has more modding capabilities due to XML, but is more difficult to mod (requires you know XML).The best Civ4 mods are practically new games in their own right. Unfortunately, many are more ambitious than successfully realised
Civ 3 has less modding capabilities due to no source code, but has much easier editor to mod through.Endless scenarios and item replacements but essentially the same game. Doesn't excite me.
As for strategy, history, and realism: there are major ups and downs to both 3 and 4 depending on exactly how much and what you are looking for precisely.
The overall game is not exactly the same, but the base of it is.
Civ 4 has many more options than 3 since it is that much newer. Civ 3 still has a vibrant communityHah! I don't know about MP or if the Civ3 plalyers have some super secret hideout but there are Civ4 mods with more vibrant forum communities than Civ3. Check out Fall from Heaven., and the size of it speaks for itself (mostly those who have reverted back to 3 from 4); usually it seems that of all users online here there are 3 times more people in Civ 4 forums than Civ 3, which is quite impressive given III's age.
For combat, neither is even remotely realistic whatsoever (anyone who says otherwise is out of their mind; for combat realism, a tactical war simulation should be played instead).
3 has a larger database of historical units because of it's age. For history, Civ 4 has the ability to mod scenarios more in depth than 3 does, since 3 you are stuck with the robust but limited capabilities of the editor.
Just so you know, I have 4 and all expansions, but went back to 3 primarily because the annoying things in 4 I felt were more annoying than the ones in 3 (most things in the I tend to hear most often list). I won't tell you 3 is better than 4, or 4 is better than 3... it all depends on your personal preference.
Tom