I'm wondering whether to use fitType = local or parametric, and why?

(1) fitType = local

https://i.imgur.com/gvQcvma.png

(2) fitType = parametric

https://i.imgur.com/fkNdOk2.png

Thanks in advance!

They look very similar. I may slightly prefer the parametric model here, because local is similar but parametric gives fewer outlier dispersions.