Both have their advantages, shield boosters provide instant relief, armour reps take a full cycle before they do anything. HOWEVER, this doesn't take into account passive, buffer or regen tanks.
For PvP, armour buffer tanking is prefferred, for PvE, you play with your skills, ship bonuses and resistances. For a ships BASE resists, you want Shield for Kinetic and Explosive, Armour for EM and Thermal; though I've managed to omni-tank a large group of Rogue Drones before now.
With shield tanking, you also know EXACTLY when to get out, when your shields hit 30%, but that's also a hint as to when to activate your armour reps too.