Unless I'm mistaken aureate phoenix increases relic boost, hence MM spell is applied to the aureate phoenix boost too. So the total production is given, for T1-T3 production boosted with MM (when both phoenix boost can apply), by BP×(1+RB+AP)×(1+MM+SP) where BP is base unboosted production, RB is relic boost (includes Mountain Halls effect), MM is spell boost (includes Elvrnar Trade Center effect), and AP, SP are boosts for both Phoenixes.
So the % increase from Aureate Phoenix is AP/(1+RB), with AP=3 for level 10 phoenix and 1+RB varying between 8 and 9.84 for max relic boost depending on Mountain Halls level. This ratio varies between 30.5% and 37.5%.
On the other hand, the increase from Storm Phoenix is SP/(1+MM), with SP=0.5 for level 10 and 1+MM varying between 1.5 and 2.06 depending on Elvenar Trade Center level. This ratio varies between 24.3% and 33.3%.
So unless you have high level Mountain Halls and no ETC, Aureate is slightly better than Storm.
I got a screen shot 49 seconds before my MM expired. Ok, so the Aureate gave 3x290 = 870 goods. So it is a 37.5% increase over just having the relic boost, a 32.6% increase with what I get because of the mountain hall, and a 21.7% increase when it is polished with an MM. Aureate boost is crap.
Here's goods cost for the tournament
So, the use of a pet food on the aureate would require 30 t1 manufacturer collections just to pay for the planks. I have 8, which I can collect twice, so a pet food would give enough extra goods to cater maybe 1/2 of one level of a province here.
If the Aureate tripled your manufacturers, regardless of whether they were polished or not, well, 2 collections of 8 polished manufacturers would give 4002 x 3 x 16 = 192k instead of 64k. At this province/level, the use of a pet food if it tripled output and you polished with MM would give about 7 extra encounters, so one full province and one level.
And in terms of these FA badges, well, it would give you the power to triple the rate you make them for two collections only, so instead of not finishing even one badge from a 3 our collection with 8 polished manufacturers, you could collect 2. That is actually a very expensive use of a pet food, so you could collect a total of 4 badges instead of about 1.5.
This is such a gross imbalance...