This one's a bit of a toughie, so I'm gonna break out the big guns: vaguely structured analysis. There's three axis of choice that seems most relevant to this vote. Those three are opportunity cost, worldbuilding, and the impact on our art Thief of Names.
Opportunity cost:
At its core, opportunity cost refers to whether, and how much, one option precludes another and what that exclusion "costs" us by being lost. Some votes have this as a real factor, some don't, and some have an uneven distribution where one choice has substantially more opportunity cost than another.
This vote is pretty straightforward on this front. Neither option is advantaged or disadvantaged over the other, and, because we're choosing how the art Thief of Names develops via this vote, the opportunity cost is 100% and I don't even need to touch on guessing which of the lore opportunities is more limited than the other. Any argument that we can swing back around for the other choice is fundamentally flawed in the full context of what this vote is about. The art development aspect locks that in as true.
Worldbuilding:
Here's, it's kind of a wash and it's going to come down to vibes for people. One way you could look at it is do we want to see the horrors the powerful unleashed on the weak, or do we want to see the horrors the powerful wrought on themselves? There's dozens of different dichotomies that can be applied to the choice, so getting too worked up about it doesn't really appeal.
On a personal level, I'm a big fan of Palace of One. I dig the vibe, I dig the incompleteness of an Ascended Law, I dig the failure of that dream, and I dig the parallels it's possible to draw between the ascension and contemporary political figures. I'd like more ammunition to craft my little comparisons of perverse irony. And, I have to admit, I'm attracted by what's forbidden. Worship of Palace of One is officially proscribed by Shenhua's decree, which makes finding guides to its nature exceedingly difficult and a guided exposure by one of Shenhua's apprentices a unique opportunity.
Lastly, the dark subject matter of the Roots is something I'm personally entirely comfortable wading into, but historically it's something that can invite derails. An example would be how even the hint of Luo Zhong pressuring Bao Qingling to join in his marriage scheme caused a firestorm which distorted votes over months, prompted a flurry of "take-back" votes, and basically caused yrs to flinch-dump the character and whole storylines even when those votes didn't stick. The things we're hinted to be looking at in the Roots are substantially worse, and while that's not a guarantee of anything, I'm not really seeing (or feeling) why what's on offer there is worth the risk or discomfort, not at the moment. Just doesn't grab me.
Thief of Names:
For me, this is the big one. Mainly because it's the subject that the decision is being made in reference to, when you really dig down to it. What lesson do we wish to pursue for our art Thief of Names? And in making that choice, I think we should look at both the impact of how the tool chosen influences the kinds of stories Ling Qi engages with and the interaction of each tool with storytelling more generally.
First off, what are the options? Just gonna copy+paste to avoid the hell of attempting paraphrasing and paragraph formatting at once.
roots: "There, you would learn of the tools which abrade a person down to their least selves," Shu Yue said. "You have learned to walk in the mind, in the personal Dream of a cultivator. Here you would learn to hurt, with the deliberation of a surgeon's scalpel."
palace: "to know the terrible, scouring fire that is hope. To know how minds may bend toward a distant and unreachable dream. And how these things may be turned. How they may be broken and twisted, the lesson the descendants took from her. This would be another lesson of sight. But as befitting the coming war, it too is a lesson of hurt, if one lesser than the roots."
Way-breaking is cool. Not only is it cool, but it's mysterious. Most dramatically, we saw Shu Yue break a Sovereign's Way with a mask plucked from his own mind, chosen to carry words of sundering Truth. We have seen sect elders at the ends of their Paths not due to age but because their Ways splintered under the tribulations of the world. Maybe most strangely, we've even heard, from Kohatu and of her Master, of clashes between cultivators bending Ways enough to reawaken humanity thought severed or lost. It's a deeply interesting field to explore, and thankfully both options touch on the subject.
The first option is focused on destructively assaulting an opponent's self-identity, though interestingly we'd apparently be gaining our inspiration via exposure to the rawest manifestation of the ways the Hui stripped and dominated the autonomy of others. The second option is more focused on perception/understanding of a target, but also has an element of using that understanding to harm them, seemingly drawing inspiration from the Hui's failed grasp at their founders' ideals.
Of the two, I personally find the second more interesting. I don't have anything against Way-breaking people, I do think it's cool, but it's not super compelling either. I prefer a "lesson of sight", and the ways in which the second option attacks people, by exploiting an understanding of their hopes, sounds more interesting and more in line with other projects and priorities Ling Qi has than just grinding somebody down. Trading some of the punch for what seems likely to be more congruent with our other efforts/storylines makes more sense to me.
But that's just looking at how things would tip Ling Qi's approach using the the art, what about how either approach would impact going on to tell that story? It's really easy to overlook, but not all vote options have the same ease of application, and it's worth examining.
No matter how you approach it, I think, Way-breaking is a narratively intensive kind of attack. You need to draw out a lot of internal characteristics from the target to put on display, not just for the in-universe function of the art, but in order to make the scene convincing for the reader. This means words, and carefully chosen ones. It's a more challenging kind of scene to write, but this is balanced out by the facts that it's really cool and that it injects some variety into the story as a whole.
But the labor-intensive nature of Way-breaking means that there are meta-constraints. We will not be Way-breaking often. Setting the foundation for one requires too much setup, usually over a spread of scenes and a whole lot of words. Even more than that, there's a fundamental tension for any author here: to prepare a victim for a Way-breaking, the author has necessarily turned them into a fleshed out secondary or tertiary character, and Way-breaking them means writing off all of the work you've put into them. That's not to say that it's not worth it or that it'll never happen, but it does mean that it's inescapably a rare treat for us.
With that in mind, it informs us of the utility-in-practice of how we develop Thief of Names here. And, again in my opinion, it shifts that analysis in favor of the Palace for two reasons, related to frequency of use and conservation of author effort. One, because Way-breakings are necessarily rare, a technique that focuses mainly on perception will simply be used more. Two, because the focus of the Palace option's Way-breaking is less total, and more aligned with twisting and manipulating hopes, it's easier for yrs to have the art's use be decisive but not write off the target character completely. There's more latitude for repurposing of that target character, and in a way that still feels like a success/rewarding for player efforts.
[X] the lesson of the palace
This is the choice that's more interesting to me personally. And as a bonus, I feel like it will be easier to write its use into the story effectively and frequently, thanks to dodging some of the internal conflict inherent to (the very cool) Way-breaking narratives.