Wood rules and tape measures are similar tools, and I've realized I almost always default to the tape measure. When should I be using a wood rule instead?
A measurement by a rule will usually be more accurate than a tape measure and will not bend. You can hold a rule against a flat object much more securely than can be done with a tape measure. Also, if you have a machinist's rule that is accurate to the end, you can scribe using the end of the rule, something that is impossible with a tape measure.
Let me spin this in a slightly different direction:
If I use a wood rule, it's because I like the feel of the wood and/or need the rigidity or straight edge. Or nonconductive.
If I use a rigid metal rule, it's because it's more accurate than a tape measure and/or I need the rigidity or straight edge.
If I use dividers, or a story stick, or something of that sort -- wood or metal -- it's because I'm measuring one thing against another rather than against numbers; again, that can be more accurate.
Nowadays, the only place I regularly see them used are with masons. Mason's rules have sizes and lengths for standard cinderblocks and bricks printed on them (for measuring multiple courses with the appropriate number of mortar lines, etc.)
I still reach for my smaller folding rule when making decorative boxes; though I might just as likely reach for a small steel square or flat ruler.