I feel like the playful death is the most common and it's the one I don't like. Sims are always skewed in favor of happy emotions so playful bumps up very quickly into hysterical with just a few interactions. I wish I could turn that one off.
The Anger death I like, I feel like it makes sense, and the death from Embarrassment is meh, but seems pretty rare, at least in my game. Death from fright and sadness would have made more sense, but because the Scared emotion ramps up so quickly, I can see why it doesn't have a death because it goes over the top all the time and can spread to other Sims. I love that Sims can experience fear, but I think it still needs some tuning, like with thunderstorms. I also wish they had allowed us to choose what our Sims were afraid of, or that fear was more connected to traits.