Shield has bigger stat bonus (depending on size) but bow has what? A high bonus to attack and spy attacks? Just about preference
Everytime I want to play skyrim it's backed up by me remembering that its very repetitive with all the cave clearing... I'll want to play it again one of these days.
Shield wins because you can use it to block the arrows while you advance on your attacker, you can then use the shield as a bludgeon to take your enemy out (because news suck as a melds weapon)
Bow no doubt it's a massive static bonus that is larger than the amount of defense added. Though shield could have its purpose