I feel like the subtitle to this post should be "two go in, one comes out, it's a battle to the death!"
These two are always compared to each other because they serve the same function in lotion making - they offer co-emulsification, they increase viscosity, and they act as fatty ingredients to add to the emolliency of the lotions. But there are some differences and they're really all about the skin feel.
I think of cetyl alcohol when I want to create a thick glidy lotion, like a body butter or massage cream. I like cetyl alcohol in anything with a cationic quaternary compound. If I'm making a conditioner or using BTMS (or another conditioning emulsifier) as my primary emulsifier, then my first choice is always cetyl alcohol: It works in conjunction with the conditioning agent to impart even more conditioning!
I think of stearic acid when I want to create a thick, tenacious lotion, like a foot cream or hand lotion that will last through washing. I think it makes my thick lotions denser, creamier, and waxier. There is some drag in it, which can be a good thing when you're using a foot cream - somehow it makes it feel more intense.
Having said all of this, I think the only way to really know the difference between the two is to try them. Try this at home! Using the body butter recipe (original post, April 3) or the modified body butter recipe (original post, April 5), or your favourite lotion recipe make two batches with exactly the same ingredients, switching the cetyl alcohol and stearic acid. (Use the same fragrance as well because we want the only changes to be the cetyl and stearic.) Label your jars well so you know which is which! Ask your friends, family members, or random members of the public to try out the lotion and give their advice!