This question is relative because it depends on the stylist, but in general, a seat that is wide enough for comfort is generally the rule. Our styling chairs are designed based on ergonomic principles and experiences taken various usage scenarios into account druing the development process.
As far as the back height that would also depend on the stylist and client but you would want a higher back to make sure the client has a comfortable experience while also not intruding on the neckline space needed for cutting.