ΔE 15.5, loose: different enough that you should pick on purpose. Middle Stone is a little lighter, more muted, cooler than Warm Brown.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 15). Middle Stone is a little lighter, more muted, cooler than Warm Brown.
The same difference applies the other way round: Warm Brown is a little darker, 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 Warm Brown on the colour wheel See Middle Stone on the colour wheel
All matches: Warm Brown equivalents · Middle Stone equivalents