Related, of course, is my strong aversion to dice in LARPs. The LARP dice situation is two-pronged: practical (rolling dice in many situations can be awkward and interrupt the scene/roleplaying) and gratuitous (LARPs have many other sources of uncertainty and randomness and I'd prefer to focus on choices and maybe skill rather than luck).
However, tabletops don't have much practical issue with rolling dice (sure, they occasionally fall on the floor, but they're also inherently fun to roll (for me)). And they don't have many other sources of randomness, being less oppositional, less real-time, and less player-skill based.
But they also don't inherently need randomness. You can do rulesless tabletop-style roleplaying just fine with the right group. But the risk is that you get two people disagreeing about whether something would work. Dice provides a semi-neutral way of deciding whether something difficult or unlikely works without resorting to voting or complete GM fiat.
But it's not the only way to do that. The Chuubo's way does this with costs. You've got Will and MP, and stuff you want to do that you're not obviously skilled enough at to do trivially will cost one of these. Contests will often be decided by how much the participants spend.
(Incidentally, Fate really ends up being a hybrid system in some sense. You can mostly succeed at anything given enough fate points (spending 4 fate points is the equivalent of moving from the worst possible roll to the best), so the roll is in effect determining the cost of success rather than determining success or failure.)
The Chuubo's system has some interesting effects. One is that it's the complete opposite side from D&D in terms of test frequency. D&D explicitly lets you retry and reroll actions as much as you want. Didn't find something your first search? Search again! (It has dedicated rules, taking 10 and taking 20, based on this.) Games like Burning Wheel and Fate tell you to only roll once for most protracted actions, like searching, but break into vaguely tactical minigames with repeated rolls for things like combat. Chuubo's goes a step further. If you're fighting someone in the same way, that's a single intention, and you spend the will once and hold it until you're done or you decide to drop it in favor of something else. You can swordfight all day with a single expenditure of Will, while in Fate that'd be a series of actions each with its own possible fate point expenditure.
This intention system is what makes dicelessness work for Chuubo's: it completely avoids any sort of minigame based on repeated actions. In a repeated action combat minigame, it'd be boring if each attack had the same result against a given opponent, so randomness is useful. By eliminating repeated actions, Chuubo's avoids this issue, and in doing so mandates a different perspective on things like combat than most tabletops. This seems like it changes the focus of the game quite a bit: if you try to solve a problem with combat, either you win quickly and move on or you fail and need to try something else; thus, the game avoids spending lots of time or attention on combat compared to many games.
It's also a bit of a feel thing. In Apocalypse World, say, it's important that any action has the chance of going horribly, even if you'll succeed most of the time. Chuubo's lets you know that, absent shenanigans, a more-skilled (well-rested) character will beat a less-skilled character, unless the less-skilled character is willing to sacrifice more. This focuses more on sacrifice and shenanigans and less on uncertainty. (This also loops back a bit to LARPs, in which a deterministic combat system encourages attacks by making a character who thinks they have the numerical advantage think they'll win with low risk, whereas an RPS system or similar can lead to more hesitation.)
I still feel biased towards dice, but I'll be interested to try Chuubo's in practice to see what I think. (I have played a little Nobilis, but I feel like the simpler system in Chuubo's could help this shine more.) Until then, I guess I'll just keep overthinking things and then blogging about them. ^_^