After all, algae (and plants) have a preference for carbon-based nitrogen compounds, such as urea.
I guess we do not know yet what plants prefer, as far as we know it seems the plant doesn't care much where the nitrogen comes from as long as it's there and the plant grows either way.
We know for example that a tomato that is grown on rockwool substrate under artificial light and artificial fertilizers might look the same but has a different and much less taste than a completely naturally grown tomato under the sun on organic soil with organic fertilizers. The Dutch tomato nurseries used to produce tons of artificially grown tomatoes to be exported to Germany for example. But they shot themself into their foot with it and these tomatoes were at one point commonly known as tasteless Dutch Waterbombs and became more and more unpopular. The Dutch growers had to adapt and return to the more organic way of growing it. Why that is, is actually a complete mystery and it's still impossible to replicate it artificially and produce the same result. Artifially grown crops are also more prone to catch diseases than naturally grown ones.
From a growing perspective in form and colour, the plant doesn't seem to care... From a health and taste perspective, it seems to care a lot...
We also know that there is much more to it than meets the eye, plants are symbiotic organisms and live and work together with other micro-organisms, such as bacteria, other critters etc. and fungi in the soil. We know they do, yet we have very little knowledge of how this complexity all works together. The bacteria and fungi etc. do not only do nitrification but also seem to produce hormones, peptides enzymes etc. and the whole underground network also seems to be a sort of communication network.
Soil research results revealed that the use of artificial fertilizers kills this underground network and makes the soil more compact and harder for the plant to root healthy. Soils that get natural organic fertilizer are much more abundant in micro-life and therefore much more loosely and easier for the plant to grow in.
So we know its existence and we know it does a better job but we yet do not know why and how it all works together. Is it the plants that prefer it? Or the entire subterranean symbiotic complex helping one another? This is still a mystery of nature. We yet do not poses the means to measure it.
So there is no definitive answer to your question...
What we know concerning organic nitrogen such as urea in a tiny aquatic ecosystem such as an aquarium a tad too much of it is rather toxic to water life. That's the reason why it's not recommended to use fertilizers containing urea but KNO3 instead. Some still do use urea and are successful with it, but it's very tricky and playing with fire and it could kill your livestock.
For the rest, anything organic is/was from living organisms, could be waste in the form of once alive and now dead or a secreted waste product such as pee and poop (urine - urea). And all life as we know it is thus organic and carbon-based.
Little fun fact
in the early days, farmers that kept cattle in their stables had their cattle urinating against the stable's walls. They noticed the walls were covered with a crystallised material. It needed to be cleaned out at one time and they scrapped this off the wall and used it as fertilizer on their land and this was/is Dry salt Urea in its most natural organic form...
Dried/crystalized cattle pee... We could do this too, just find a nice spot at the garden shed and keep peeing long enough against it. Then you'll have your DIY nitrogen fertilizer.
