Although Destruction is most certainly not a "fire and forget" type skill like Archery, I don't use the two together. Given that bows require two hands and can do ranged damage, it seems a bit superfluous. I prefer Destruction, though, due to its versatility, elements and effects. Honestly, I cannot imagine a build that uses Destruction and Archery being fun or even useful.
oh, it can be. you can use archery and destruction together quite well. Archery is good for stealth, extra-longe-range, or even medium range, and things like that, but in a confined space, what use it is? melee enemies will deal a lot of damage while you draw back the bow. this is where you use magic. for closer enemies, or the ones that move around a lot (like those pesky dragons that insist on eating you), you can use a steady stream of magic to catch them, and follow their movements, rather than guessing where they'll be. plus, you can lay traps behind you, or drain their stanima/magicka to weaken their attacks. also, Destruction improves the power of enchantments like Shock Damage, i believe. if so, put Frost or Shock damage onto a bow , you can do extra damage while draining stats. with 100 enchanting, you can add both to drain health, magicka and stanima severly with each shot.
both hace ups and downs, but can be used together well. cloak spells are helpful in tight hordes of enemies.