Is it better to build new rooms or upgrade rooms in Fallout Shelter?

I am wondering which is more efficient in the beginning: building new rooms (production specifically) or upgrading existing rooms? Assume that the rooms are already three wide and that I would (obviously) be upgrading them all at the same time. I am trying to figure out what will get the best return on investment right away.

The main reason I'm wondering is that in my vault I'm going for 3 layers of the following (power, food, water), followed by several layers of med/rad labs for mass-storage purposes, training rooms, etc. I'm trying to quickly build up a solid base of the first three and wondering what the most efficient method is between upgrading (3 rooms) and building (3 rooms).

It seems that building more rooms might be better as it would probably get more in the long run (two rooms vs one) even with the bonus of upgrading. However, it does get more expensive to build rooms the more of one that there is. Coupled with the upgrade bonus, would this make it worth it to simply upgrade before building more?

Additionally, at least in the beginning, it is difficult to store up enough caps to actually upgrade due to expense. Would this make it more efficient to simply build more rooms, even with that additional expense?

First off, I know similar questions have been asked before; however, they usually don't really mention what I am looking for specifically (efficiency).

Thanks!