I also agree with that the tale of the Iron King would be harder to uncover than the tale of Gates, but there's a chance that, like with the ES and Tsu, their history is full of absurdities compared to the real truth, so hearing from the source sounds better imo.
But then the Tale of the Iron King also sounds like good prep for the summit and Grandpa Nightmare, since Dreaming Songstress is about the engine that drives mankind.
And then both of them work with Xuan Shi. Like I said earlier, this feels like it's connected to the difference between sacrifice given and sacrifice earned. The Gates fits the first one, and tells him about the White Sky in general, which can help convince him to join us.
The second one is about sacrifice forced onto others to help the Iron King, and gives a view into the current WS politics, which can also help convince Shi to help us because he refutes Grumpy Sword.
One thing to keep in mind though is that this choice is related to Shi and his insights in Narrative. Which option fits Narrative? Both do. Which option fits Shi and his current plot with Narrative? Both fit him to some degree, but which fits best? I'm not too sure about that.
Edit: I would like to note that Gates being foundational can *also* help with the summit. Foundational tales can give a lot of insight into a polity, culture, and how it's advanced over the years, like with Tsu bringing people together (the ES is now fractured), the Peaks with the Sage Emperor and dragons (no explanation needed), the Bai (no explanation needed) and the Zheng (no explanation needed)