Gosh, I can't believe how many smart guys are getting the logic of these buildings WRONG!
First of all, let me say that these buildings are the greatest thing since sliced...er...bureaucrat...if you're Drengin.
Second, everyone please note that although there are similarities, the RCC and the power plants are NOT alike.
The power plants begin to be available very early in the game, IF YOU CHOOSE to research them; they require a separate research effort. In additon, they are relatively cheap to build, compared to a similar tech-level factory, but have fairly stiff maintenance (3).
The RCC does not require a separate research effort because you gain the ability to build it when you develop Research Academies, in the main research tech branch, but by the same token it is probably not available until mid-game, when the similar level lab is providing a healthy hunk of tp's (12 from an RA). The RCC is expensive to build compared to an RA (300 vs 150), but the maintenance is cheap (1 vs 3/wk).
Third, note that both types of development amplify the respective applicable capability points of the planet, that is power plants multiply mp's and RCC multiplies tp's. They DO NOT just multiply 'factories' or 'labs'. This is key.
On your homeworld, you start out with 24 tp's and 24 ip's from your Civ Capital.
For research, since the RCC is hard-linked to the know-how to build Research Academies, after your first 2 labs on the homeworld have upgraded to RA, the RCC should be the next research building you build, even if you have to replace an existing lab to do it. If you have even one lab on a bonus tile, the RCC should be the very next thing to happen after that one tile upgrades. It costs a bit more to build, but it pays it back in maintenance in 75 weeks, and after that its gravy.
Just labs: Civ Cap (24) + RA (12) + RA (12) + RA (12) = 60 tp, 9bc/wk maint.
With RCC : Civ Cap (24) + RA (12) + RA (12) + RCC (25%->12) = 60 tp, 7bc/wk maint.
W/ bonus : Civ Cap (24) + RA & 100% (24) + RCC (25%->12) = 60 tp, 4bc/wk maint.
For production, it isn't quite so simple. If you have developed/traded/stolen Fusion PP, and you still only have Basic Factories, it makes marginal sense in terms of production numbers for the Fusion plant to be the 5th industrial structure you build, but you will pay a maintenance penalty for it.
Civ Cap (24) + BF (4) + BF (4) + BF (4) + BF (4) + BF (4) = 44 mp's, 0 maint.
Civ Cap (24) + BF (4) + BF (4) + BF (4) + BF (4) + FPP (10%->4) = 44 mp's, 3bc maint.
If you have a couple of Basic Factories and one of them is on a 300% or, God bless it, a 700% bonus tile, then the FPP should certainly be your next industrial build.
If you are already building/converting to full Factories, which produce 6 mp's each, then there should be an equivalent of at least 6 Factories in production before you build the FPP...but that will happen if you have a Precursor Mine. Other wise, wait to develop the Anti-Matter PP before you build one.
For the Anti-Matter PP, production levels break even if you build the APP in addition to just 1 full Factory. With more Factories in play, you gain an actual weekly mp benefit from having the APP on-line. There's still a small maintenance penalty until you reach Manufacturing Centers (level 4 'factories'), or when there are large numbers of Enhanced Factories (level 3 'factories')
Civ Cap (24) + Fac (6) + Fac (6) = 36 mp's, 2bc maint.
Civ Cap (24) + Fac (6) + APP (20%->6) = 36 mp's, 4bc maint.
I'm not going to do the slightly more complicated math for the colonies; but it would be similar, with a somewhat later beneifit point in the development sequence of the colony, since the Colony cities only give 10 tp's and 16 mp's to start. Any primary production structures on bonus tiles can make the support structures a superior immeadiate choice of improvement.
The bottom line is there always is a big benefit to building these things, from almost right away for the RCC to ~mid-game for the power plants.
drrider