Those are cool screenshots. I agree that, in general, capturing a city is better than building the extra Theatre. Because you get that, a city, instead of a Theatre.
It's especially true when you are dealt a single direction for expansion, as in this case : if you want to get more land, you need to roll over Gandhi.
I've never played K-Mod but I did read the changelog. Ok, the actual culture output of a city has more influence over tile control.
Here : Gandhi peace-vassaled to Mansa Musa and, likely, immediately turned his culture slider up.
So, your cities produce 9 and 3 culture per turn, they're isolated on the frontline (backline cities don't help them protect their tiles). His 2 forward cities likely produce 50+ culture per turn, possibly 100+. Hence the disaster.
The point I'd like to make is that : you can fight culture wars but you didn't. 3 and 9 culture really isn't much. 9 culture is what ? 2 religions, and ancient library and a theatre. Not much of an investment. (Given that, your reaction to build maces and knights was correct !)
If you're going going to fight a culture war, you know it early : borders have been established and you don't intend to invade.
Therefore, you can invest early in cultural buildings, best of them being wonders and cathedrals for multipliers, then you have civics like Free Speech. You can also settle support cities 3 tiles behind to help push the borders.
Then you can have juicy stuff like :
- early on, the Sistine Chapel (does Gandhi have it ?). Suddenly, your Temple/Monastery combo gives you 13 culture per turn ;
- later on, corporations. Some corporations will easily give you in the 40 culture per turn.
In BTS, the core of the matter, is to settle cities so that they help each other. If you have a couple of cities producing culture on a tile, you're that much more likely to hold control. It gives you time, before an invasion, at a low cost (not hundreds of hammers spent on buildings).
This is from a culture war :
I'm not saying : go found corporations. Rather, I'd point out that it's hard to get a high culture output from buildings alone. A Library maxes out at +4, it's not much.
Multipliers matter. And they matter the most if you or the AI are going to use the culture slider : in this screenshot, if I turn my culture slider to 50%, that's another 100 culture per turn in this city. How do you get 100 culture per turn from building Libraries ? You don't, you just can't.
It isn't advisable to toy with the culture slider, other than for culture victories, but it goes to show the relative importance of things, as far as the final output goes.
Note that this city doesn't even hold control over all of its tiles (!). (Sushi is new - it won me that war - but still.)