What difference do they actually make? In what cases do you want steel picks?
Firstly, value is affected by the material. A steel axe will cut down trees just as well as a copper axe, and a steel pick will mine stone just as well as a copper pick. However, in case of combat the material will make a big difference. Steel picks are pretty good if your miners get ambushed (note, however, use of a steel pick in combat trains the "mining" skill). In the more recent versions, not only will some materials perform better against others, but I believe the wear and tear suffered by the weapon will be altered, as well as the wear and tear inflicted upon armor.
This means copper weapons against iron armor will not last very long, while steel weapons will fare quite a bit better. Blunt weapons are best forged out of other materials, as damage used to be based on the density. The preferable material used to be silver due to it being the most dense material you could forge a weapon out of under normal circumstances. However, since wear and tear went into the game, this may have changed.
Outside of weapons and tools, the material used affects the weight and value. The former affects hauling speed, as well as blunt damage in case the object ever crashes into something. If a solid gold minecart crashes into someone, expect injuries. You can shoot gold statues or gold bars out of a minecart gun, and any creatures in the way will take an enormous amount of damage. The latter makes some things better or worse for trade and dwarves who have these items in their room may be more happy about them. Dwarves have material preferences too, so if a dwarf likes schist, they will get a bonus to happiness on top of the normal bonus given by the standard value.
Items made out of wood will generally burn if they end up in contact with fire or magma, and some materials are magma-safe. If you have an area in the fort that either handles magma or lava, or is expected to come into contact with magma or lava or a regular basis, consider making the furniture within out of magma-safe materials.