Its sorta works both ways.

Strictly speaking, from an "OB" perspective, the cost will be the same.  Ie, building all up to 300% in one go, or building from 100% to 200% and then to 300%, it will cost the same.

The difference however comes in the form of the other factor, "Large Empire Cost".

While building from 100% to 300% in one go, you have the Networth of all the buildings at 100% and so will have a smaller Large Empire Cost (which is just a percentage increase).

If you build only to 200% thats fine.  But then from 200% to 300% you'll have the networth of all those extra buildings.  Your empire will be bigger and you will have an increased cost there.

And this is aside from the fact that with the more networth, you'll have less research in Construction Bonus (because its based on how big you are), and so by having more buildings and more networth at 200%, you'll have less research and again, it'll cost you more.

Hope this helps and makes sense.

Thanks Torqez. I can see it all very clear now.

Agree with Torqez.
I often do the OB depending on planet size, constr reasearch and large empire penalty. Some intersting thing you must know is you better start building your infra in the same tic you get the new planet (by explo or by force) bcause nw isnt still counted until next tic so you can build cheaper.
Notice if you get 20 new planets swapped from a fam member and you wait for next tic to start building then your contruction bonus research will go down and your large empire penalty will go up, so your building price is more expensive.

Often you can full build planets and then once buildings come you double them, as example, a big planet sized 312 you can build 300 first and then double to 600 without OB costs. I Often get each planet to a basis of 500 buildings, no matter what its size is, OB costs arent really high to get each planet to 500 buildings, and then, as your economy grows you start doubling to 1000 buildings starting with the bigger planets so OB costs arent much high. Then depending on your progress and the lenght of the round you can double to 2000. Building more than 2000 per planet isnt really productive since the spent on iron is extremely expensive, but if you are in a top fam and the round is long enough you can evaluate the benefits of putting your biggest planets at 2500 buildings. Then you get a mention for "Biggest Infrawhore of the Round"

personal preference i just like to double up my infra on a planet if i know im filling it up at once

0 - FB - 100% - 200% - 400% - (either 600 or 800% pending on if in PW or Capri, respectively)

also should note that you should always try to keep in mind how long it will take for your infra to pay itself off, to decide how much to build, when, or if at all

indeed. even if u go 0 - FB - 100% - 200% then the next shud be 500%