It depends a lot on the translation I suppose, because my experience with the old testament was rather unpleasant - reading it in centuries-old language brought me no joy at all.
Another factor in my naming it the probably #2, after Gilgamesh, though, is that everything else is just that bad to a modern reader, so the OT looks pretty damn good compared to all that, even if you're stuck with the King James Version. My favorite story from ancient Egypt[0], I wouldn't recommend to many readers, because damn, it's a slog, and it's still an easier read than some of the others, or than anything I've seen in Sumerian or Akkadian (Gilgamesh excepted). It probably tells better, as a joke (it's a comedic story), than it reads, if you had someone really talented telling it.
That's typical for other Near Eastern literatures, too. Lots and lots of repetition, is the main problem for a modern reader, as far as the prose goes. Much of it also doesn't really relate a story, exactly, and the cultural and religious references are obscure at best. You don't even get mythology, really, for the most part. Prayers or incantations, sure, but there's no Hesiod or Ovid of Sumerian religion. There's a little of that, sure, but it's very fragmentary and you have to bring a lot of context from outside of it to make much sense of what you're reading.
For the millennia(!) of texts we have from Egypt, for instance, there are only a few short (and often fragmentary) works that we'd recognize as stories. You have to settle for reading a variety of non-fiction or semi-fictional genres to get much more out of it—"mirrors for princes" and scribal didactic texts, which are probably the most interesting of the lot, plus endless formulaic and not-especially-illuminating funerary texts, and a good deal of historical propaganda about military victories, mostly from monumental inscriptions, almost all of which are intensely boring even if you're really into military history. And that's probably the richest literature we have from that region in the pre-classical period, at least as far as what's available in English translation.
[0] The Eloquent Peasant
The Eloquent Peasant is a fascinating little work. For those who aren't familiar with it, it's the story of a peasant who owns a donkey. There's a farmer alongside the road who has allowed his crops to grow right up to the path, knowing that passing draft animals will occasionally eat his crops. This allows him to take the owners of the animals to court, including the peasant in the story.
But when the peasant arrives in court, he speaks with great eloquence. The judge is so impressed that he decides to drag out the trial to hear more of these speeches. He sends off a note to someone important (the pharaoh or the governor or someone), saying, "Hey, you need to hear this guy!"
The peasant, assuming the court is corrupt, gives another speech about the importance of honest courts. And so it continues, with the peasant holding forth on justice and government.
It's a brilliantly subversive little tale. The core of it is political rhetoric. The "framing story" is an amusing tale about a peasant with a donkey. And the officials in the story are secretly delighted by the peasant's eloquent speeches about good government. It's a way to discuss politics without making the pharaoh look bad, basically.
By ancient standards, it's pretty remarkable. The framing tale and the subtle subversion feel more modern than other works from that era. But as the parent post suggested, it would probably work best told as a tale by someone who could switch between the humor and politics.
(I think we have a progressive tendency to overestimate the sophistication of our age relative to those of the past. And not to be pedantic, but I wouldn't call what you described as subversive. Subversion would involve destroying or undermining a just political order. But offering a gentle reminder of the importance of justice is counterrevolutionary because it seeks to restore something good. We must not relativize revolution as merely that which is opposed to some prevailing status quo.
Socrates was not subversive; the sophists were.)
Is the repetition a clue that maybe these poems were meant to be sung, and not read?
In a way, Sabaton can be considered to the modern-day bard, singing in Metal.
Indeed, it's been my observation that the written register has almost entirely disappeared - there's only the spoken register in text form. But even that has declined in complexity: consider what Presidential addresses use to look like. Go compare Lincoln's Second Inaugural address with Obama's, for example.
> Indeed, it's been my observation that the written register has almost entirely disappeared
I think that's a lot of it. Then again, maybe people in the 19th century US spoke like that, too? I haven't looked into it. Surely there's a book about this....