ΔE 24.1, loose: different enough that you should pick on purpose. Pearl White is noticeably lighter than Mithril. They are different kinds of paint: Army Painter Mithril is a metallic and Tamiya Pearl White is a pearl paint, so they won’t behave the same on the model even where the colour is close.
Can I use Pearl White instead of Mithril?
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 24). Pearl White is noticeably lighter than Mithril. They are different kinds of paint.
Can I use Mithril instead of Pearl White?
The same difference applies the other way round: Mithril is noticeably darker.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.