I've learned both increase heavy armor skill and light armor skill enchantments from breaking items, and I would like to know whether using them has a noticeable effect or not when enchanting a piece of armor (or ring or necklace), say in the formula used when calculating the damage reduction.
Do they have any effect in reducing the damage taken? Are they worth using or other enchantments (health regen, stamina regen and so on) should be chosen instead?
There will be an increase up to the maximum damage reduction possible which effectively blocks 80% of damage received. However I suggest using other enhancements depending on what you want to achieve with your character.
Damage Reduction from armour can be maxed out via smithing on heavy armour (light armour requires a shield to max it out too), this is with maximum armour and smithing skills. This will also require the top tier armours too.
Even if you don't have the maximum level skills, you can use Fortify Smithing enchantments/potions to get the maximum armour damage reduction earlier and with lesser armour types.
