By 止す, do you mean よす? It is almost always written in kana alone. Besides, 止める has two readings (とめる and やめる) and two meanings. Which do you refer to? You have to choose the right verb depending on the intended meaning:
- とめる: to stop doing something (that is already in progress) / to stop (a physically moving object)
- やめる: to refrain from doing something (usu. before starting it) / to quit (a habit, a company, etc) / to cancel (an event)
- よす: to refrain from doing something (usu. before starting it)
As you can see, よす and やめる can be interchangeable when they mean "to refrain from doing something".
Let's (change our plans and) not go.
Why don't we think twice?
I think there is no difference in terms of fanciness or register. It is natural for anyone to use them, both in speech and in writing, as long as they are used correctly. The only difference I can see for now is that よす is almost always used in the context of requesting or suggesting. 彼は冗談をやめなかった is okay but 彼は冗談をよさなかった sounds awkward to me.