Barren Yellow vs Sulfide Yellow

How close are they?

ΔE 19.4, loose: different enough that you should pick on purpose. Sulfide Yellow is noticeably lighter, more saturated than Barren Yellow.

Can I use Sulfide Yellow instead of Barren Yellow?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Sulfide Yellow is noticeably lighter, more saturated than Barren Yellow.

Can I use Barren Yellow instead of Sulfide Yellow?

The same difference applies the other way round: Barren Yellow is noticeably darker, more muted.

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.