Fowler says to avoid -ion words to describe a state or quality and to instead choose -ness words for this purpose. -ion should describe a process or action.
Yet he writes:
So far as the words are used with overlapping meanings, preciseness is differentiated by implying the importance of precision is exaggerated. Preciseness rather than precision is the attribute of a precisian.
So what does this mean? Merriam-Webster also seems to say that preciseness carries "so strong implication of severity or strictness", and gives an example as "there was a certain amount of preciseness about the young man".
What do you think is the best choice? By ear, I was just going to replace preciseness with precision.