ΔE 15.8, loose: different enough that you should pick on purpose. Eldritch is noticeably darker, more muted, cooler than Hexwraith Flame. They are different kinds of paint: Citadel Hexwraith Flame is a one-coat contrast-style paint and Formula P3 Eldritch is an opaque base/layer paint, so they won’t behave the same on the model even where the colour is close.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Eldritch is noticeably darker, more muted, cooler than Hexwraith Flame. They are different kinds of paint.
The same difference applies the other way round: Hexwraith Flame is noticeably lighter, more saturated, warmer.
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 Hexwraith Flame on the colour wheel See Eldritch on the colour wheel
All matches: Hexwraith Flame equivalents · Eldritch equivalents