Lunars have much the same as Solars, though they can accumulate "Permanent Limit" due to their Wyld taint, causing them to become monstrous Chimera.
Dragonblooded have it fairly mild, their personalities just get influenced by symbolic traits of their elements. Air Aspects getting detached, Fire Aspects becoming passionate, etc. It varies depending on their core Virtue, though, so a Valorous Fire Aspect is going to get confrontational with their passion but a Temperant one would get all weirdly ascetic.
Abyssals have Resonance, accumulating the anger of the Neverborn directly every time they act in a way that isn't suited to a nameless avatar of oblivion. Once it builds up enough, it discharges and can harm either themselves, their surroundings, or the people they care about in various ways.
Alchemicals have Clarity, not actually a part of the Great Curse but an equivalent caused by the tension between their human soul and the Primordial Essence that fills them. It makes them more robotic and starkly utilitarian, and it rises and falls with your typical humanising/dehumanising decisions as well as installing some Charms that make them more mechanical. There's no Limit Break state, though, and it actually caries some benefits as it rises.
Infernals get Torment whenever they disobey the Yozis or just suffer extreme mental stress. Some charms can increase Torment, too. When it hits a certain, they get punished by the Yozis in various ways appropriate to their Favored or Caste Yozi. Acting like a cartoon supervillain can reduce Torment. Devil-Tigers still get Torment, despite being freed from the will of the Yozi, because it was actually an inherent weakness from the Great Curse that the Yozis were just taking advantage of. All that changes is how they're punished for going over the limit, their own power turning against them instead of being smacked down by their masters.