Ark module vs Infrastructure?
When is one more valuable/desirable than the other? When is it better to use the Ark over just shipping Infrastructure over? I've never played around with Ark modules, but I'm planning on starting a new campaign soon. Been way too long. This is something I've been curious about since they were released.
Basically any time you're dealing with Venus-type worlds.
I'm sure someone's actually done the math and can give the exact CC where one overtakes the other, but I don't know it.
There's no absolute, exact CC where Ark Modules become better. Cost-wise, Ark Modules cost a bit more million pops than the infrastructure for a CC=5.0 world, so for a world with a CC greater than 5 you definitely want to use Ark Modules if you can. However, for somewhat lower CCs even if Ark Modules cost more than the infrastructure for the same population, Ark Modules may be preferable since they require no population dedicated to agriculture, so you get a larger manufacturing fraction for the same total population with Ark Modules. This is why the crossover point is not exact, in one situation you might prefer to save the build costs but in other cases while in another case you would rather maximize population efficiency. I would guess that the approximate crossover point is around CC 4.0 or so, or basically the maximum CC of Mercury. If you are really starved for population, though, it may be the right choice to use Ark Modules even for worlds with CC 2.0 or better, just to avoid the agriculture fraction.
One other consideration is terraforming. Infrastructure-based populations can remain on a planet after terraforming, and that infrastructure will become more efficient during the terraforming process allowing you to ship in additional colonists while terraforming is ongoing. This means that once you've terraformed a planet, you already have a large population in place and you can move the infrastructure to the next colony site. Ark Module populations remain at a fixed size per module, so you can't grow the population on a planet in anticipation of reaching zero CC (although once you do, you can unload the Ark Modules onto the planet surface and send them back to pick up new pops from the home world, so you won't be starting from zero). I would suspect that this means infrastructure is better when you use ground-based terraforming installations (which are cheaper at 300 BP each). Of course if you use the more expensive orbital terraformers (500 BP per module) then this is a moot point.
One last note: given that the "effective" crossover point is probably around CC 4.0, and LG infrastructure costs twice as much as regular infrastructure, once you have Ark Modules there is very little reason to use LG infrastructure except in rare cases where there is a low-gravity world with a CC less than 2 (or if you're terraforming low-grav worlds; remember that there is always a minimum CC of 1.0 for low-grav bodies, though).