Short answer: really kinda depends.
Long answer:
LETS DO THE MATH!!!
A branch office is 2 ES (Empire Sprawl/Size) while a District is 1 ES. From all variables being at their base and assuming robots are not included in the equation, here is a list of what 2 Empire Size can get you in terms of resource districts:
1 Agri District & 1 Mining district (-2 energy total) provides 2 farmers (+12 food) and 2 miners (+8 minerals) and housing for them. Since 4 worker pops need a total of 4 food and 1 consumer good (1 mineral), this means the net result for 2 ES is: -2 Energy, +8 Food, +7 Minerals.
Another possibility:
1 Agri & 1 Generator (-2 energy), +2 farmers (+12 food) +2 technicians (+8 energy). 4 pops eat 4 food and 1 consumer good. Result: +6 energy, +8 food, -1 minerals.
So in total:
1 Agri 1 Mining: -2 energy, +8 food, +7 minerals.
1 Agri 1 Gen: +6 energy, +8 food, -1 mineral.
2 Agri gives: +16 food, -2 energy, -1 mineral.
1 Mining 1 Gen: +6 energy, +7 minerals, -4 food.
2 Mining: +15 minerals, -2 energy, -4 food.
2 Energy: +14 energy, -4 food, -1 mineral.
For basic resource districts, the net gain trying to balance resources seems to typically be either +9 or +13 raw resources.
What this means is that when it comes to raw resources, a branch office is worth more than 2 rural districts once it would create about 15 energy, assuming base values for everything.
Cities districts get more complicated for a few reasons. As a whole, they are valuable for housing for specific buildings. This is where they shine, as they can house an entire factory for example, generating lots of alloys. Usually this means city districts are in fact worth a lot more when comparing to branch offices. They also get dramatically better with tech and traditions.
But if your workers have high living standards or nutritional plenitude and generally have a higher upkeep on food/consumer goods, then Branch Offices are almost ALWAYS better than districts, assuming the target planet wasn't settled three days ago.
Branch offices provide value equal to half the trade value on the planet. This varies wildly, but typically I find that low pop planets give 1-10 energy. A planet with 100 pops gives upwards of 100-200 energy. You also get the highly valuable buildings at 25, 50, 75, and 100 pops. This means that a branch office scales in value with the size of the planet (if that wasn't obvious).
And this is where the math goes bonkers. See, empire-wide bonuses affect all resources from branch offices, but naturally they do NOT receive bonuses for specific jobs. Meanwhile the base values for jobs and districts improves throughout the game. You can get (as of 2.2.5) +60% output for rural jobs from basic technologies targeting those jobs. Specializing a planet (giving +5% to specific output) and building the "resource building" (the ones that give either +15% or +25% to raw resources), and then +30% from 100 stability, and THEN combine your ascension paths, this means that late game jobs can potentially provide something like +150% to resource output.
This means mid/late-game, Branch Offices are probably going to need to provide at least 45 energy or 30 energy and a building slot before they're worth the Empire Size compared to Districts.
BUT End game? Just research +15 Admin Cap over and over. Each time you research it that's another 7 or 8 branch offices, or 15 districts, or whatever you feel like spending it on.
(Note on TRADE value: jobs are not the only source of trade. Pops also generate trade value based on their living standards and stratum, but I can't find the exact value anywhere on the wiki or in-game, and it seems to be extremely tiny. A brand new empire I started up had 2 rulers, 7 specialists, and 15 workers. The pops generated 4.80 trade. I switched to social welfare, it went up to 6.30. Utopian Abundance brought it up to 9.60. Based on those values, If it's based purely on how many consumer goods a pop eats, then a pop that eats 1 CG gives 0.4 trade, a pop that eats 0.5 CG gives 0.25 trade, and a pop that eats 0.25 CG gives 0.15 trade. BUT it may very well consider the stratum of the pop and the precise living standards or some other weird complicated math that I simply don't have an easy way to check. Aaaaand "Gospel of the Masses" makes EVERYTHING HARDER because it ALSO affects trade value from pops naturally but only if the pop is spiritualist! I think I read somewhere the value is a flat 0.25 per spiritualist pop, but don't quote me on that.)
Ok, maybe my mistake was in taking Temples of Prosperity as first buildings.
Is it worth to go beyond administrative cap?
OK, now THAT'S an even BETTER question!
No, do not build Temple of Prosperity first. People question building it at all in fact. It provides YOU with 1 energy from the 6 trade produced by the job divided in half then subtract the -2 for upkeep. Over a long period of time, it may increase trade by a bit. But if it was already a hyper spiritualist empire then it basically just gives you 1 energy.
As for going over Admin cap....actually lemme take this to a new comment.