Neither are really "organic". Fish however, are pretty organic.
Few got into this hobby to keep plants only, that's often a secondary interest, so most like fish 1st, then get into plants second, the entire balanced concept goes back to fish and plants cycling the N and P. Non CO2 tanks do this effectively.
For an EI based NH4 approach, the equivalent NO3 is about 0.8 ppm per day vs NO3 at 3-4 ppm a day. Not likely anyone will ever require more than this.
Also, short term growth fertilizer studies(often 8 weeks or less), really does not show the entire seasonal change the plant goes through or adapts with water levels in natural systems.
Some species might appear to prefer a ratio of more NH4 to NO3, but it's impossible to dose just pure NH4 to plants, there's always going to be a ratio of NO3 to NH4, and measuring it is not easy either.
If you N15 labeling, then you can do this.
So the NO3 will be labeled with N15.
Then another test will label the NH4 with N15 also.
Then you dry the plant tissue and measure the N15 the plant retained.
You can vary the ratios and then see which ratio provides the best relative rate of growth for that species.
This entails a lot of work for 1 species, let alone many, but it's fairly straight forward in the conclusion.
Feeding fish also adds N, roughly 90% or perhaps a tad more goes into NH4, then NO3 after the bacteria get some of it.
So if you know the ppm's of N in the food source, you can measure the NH4.
Fish growth and N retention is well studied, so the 90% seems fairly good for the amount of N waste from food.
If you dose say 1 teaspoon of KNO3 three x a week to a 90 Gallon tank, you can cut with 1/8th of (NH4)SO4 and take 1/8th of the KNO3 out.
1/8th to 1/4th of the KNO3 volume.
(NH4)2SO4 has no NO3, so you can manipulate each to produce a wider range of ratios FYI.
I did this, hummm......maybe 10 years ago? It was before I went to Santa Barbara, so pre 2000.
Jobes sticks and osmocoat etc also have NH4 etc.
Just do not exceed about 0.8 ppm per day of dosing.
That's the upper bound I found for non limiting N for a wide range of plants.
Many tanks will use less, but many are fooled because it disappears so fast due to bacteria also, so they assume it's all plant growth, no, not always.