ΔE 22.7, loose: different enough that you should pick on purpose. Natural Steel is noticeably darker, much more muted than Emperor's Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Natural Steel is noticeably darker, much more muted than Emperor's Purple.
The same difference applies the other way round: Emperor's Purple is noticeably lighter, much more saturated.
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.
See Emperor's Purple on the colour wheel See Natural Steel on the colour wheel
All matches: Emperor's Purple equivalents · Natural Steel equivalents