Waaaarghbobo, lead writer on Illaoi, has spoken about Nagakabouros on a few occasions here and there and, while he hasn't given any clear answers (indeed, I would say that Nagakabouros being something that the human mind can only ever perceive a fragment of is part of its intended mystique) it does paint a semblance of a metaphysical picture, as it were.
Nagakabouros seems associated with life and with living beings and with the cycle of life and death (and therefore souls). It is said to transcend dimensions and that to destroy it one would need to destroy the universe.
I see Nagakabouros as akin to time or space except, where time and space do not necessarily translate to the other planes of existence (spirit and celestial), Nagakabouros does. In our world, we have four fundamental interactions. In the IP, we have (at least) one more if that makes sense, it is Nagakabouros which seems to be the cycle of life in all its entirety (or maybe, the tendency for life to emerge and become sapient and feeling as if some higher evolutionary/creative calling in the setting).
Illaoi's religion believes Nagakabouros has a plan for the universe and that following one's passions advances that plan. They may yet be proven right. Or maybe, Nagakabouros' nature is so all-encompassing that it can't even properly perceive (or if it can, does not necessarily care for) mortal life. Is a person aware of each and every bacteria living in their guts?
I do not think Nagakabouros is a spirit god. It does not appear to be a product of human faith or myth nor does it seem significantly shaped by worship even if its connection to the spirit realm seems undeniable. Buhru's culture and religion may, however, "color" how they channel its power hence the watery tentacles vibe. It is not necessarily what Naga is (if it even "is" in a physical sense, I imagine it exists in all things as a fundamental tendency of creation). It doesn't even have to be sentient in any way that humanity can fathom because the importance of Illaoi's god is not in itself but in how Illaoi (and the people of Buhru) draw and interpret it.
With that said, Buhru worship could have potentially birthed a spirit that reflects their own attempts at describing their deity, a "fake" Nagakabouros born of human thought. Always an exciting possibility.
So yes, out of the two options provided the second seems the most apt. Except, whereas Aurelion Sol (and possibly his "kin") seems to be a purely physical (but extraordinarily powerful) entity (some things may always change), Nagakabouros is a metaphysical power. It is more a pure force of nature than a human construct or a single powerful individual entity or an anthropomorphic personification. It is intertwined with reality in every single one of its magical facets. (Note that this is my own attempt at describing it. Like I said earlier, there are no right answers yet, if ever.)
or it is a stronger cosmic entity than aurelion sol who created life.
Aurelion Sol did not create life, to be clear, although he did enable the conditions for at least some life to emerge. Odds are, Aurelion Sol himself is not aware of how Runeterra truly came to be by the world rune using celestials that crafted it and/or why they would do such a thing (although the planet is now of great interest to him since Targon's hold on him is weakened there). Could they have chosen a different star to do so or is there something special about the sun and/or Aurelion's own method of forging stars? That's a good question.
A few sources and good posts on Nagakabouros, here:
On Nagakabouros faith:
"A god's appearance is limited only by those observing it" -Illaoi
Illaoi's power:
Illaoi is powerful because she is personally capable of serving her god--- that's actually a rare gift. That puts her on the same level as Moses at the very least. Channeling her god's power (not generating it) is extremely difficult.
(...)
RE Aol Sol vs- Nagakabouros:
Aol Sol is, at best, a demi-god-- he serves only one reality and exists on only one realm.
He mocks humans because they are as small to him as mites to us.
BUT comparing him to Nagakabouros is like comparing a dung beetle to the theory of relativity.
He's just pointing out he has a better view in the rug.
Here:
AOL SOL:
Here's the thing:
Aol Sol made stars. Check.
Aol Sol made a bunch of stars. Check.
Aol Sol is super old. Check.
Aol Sol is the only dragon. Nope.
Dragons are Gods. Meh. (see below)
Aol Sol does not reflect a universal reality or truth.
Aol Sol does not exist or travel between planes.
Aol Sol can be trapped, contained, and controlled.
Aol Sol can die in some ways. (Though does not age)
Ultimately he is "A True Dragon." An extremely powerful being. Is that a type of god? Meh...
The definition of a god is pretty flexible (based on different cultural norms) So he could be depending on your point of view.
He is super-powerful.
He has been worshipped as a god.
NAGA:
Illaoi's god is not the only god. (See above: God is a tricky term).
Nagakabouros is not even the only god worshipped in Buhru (though it is the most popular on that island).
Illaoi's religion is about life serving the universe. But Nagakabouros is see as bigger than that goal.
Illaoi knows, she can not comprehend her god or it's plan. So she and her religion are attempting to serve and understand a small portion of that god idea.
She is aware that Nagakabouros is a mental construct based on human's limited perception and intellect -- but it is an attempt to illustrate a greater truth (See Brahma vs Para Brahman for an example of this.)
I did a lot of research on pre-christian faiths and Hinduism when creating this religion. Our real world pantheistic religions do not (and did not) believe in individual gods in a childlike way. It was/is a very philosophically complex view of the universe, where elements, and ideas are broken down and given constructs to hold greater concepts. Those constructs exist as dualities == both a truth and as mere symbol of a higher truth. (Thus the signifier is viewed with equal import as the signified)
Using those definitions (which is how Illaoi sees the world). A god is not simply "a being of a particular power level" it the reflection of an abstract truth.
And:
It's unlikely he could defeat Nagakabouros, he would need to end the universe.