ΔE 26.2, loose: different enough that you should pick on purpose. Old Gold is noticeably darker, much more saturated than Dwarven Iron.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 26). Old Gold is noticeably darker, much more saturated than Dwarven Iron.
The same difference applies the other way round: Dwarven Iron is noticeably lighter, much 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.
See Dwarven Iron on the colour wheel See Old Gold on the colour wheel
All matches: Dwarven Iron equivalents · Old Gold equivalents