In reply to Jon Stewart:
Fair question! They do different jobs:
Spikes on your feet aim to stop you slipping but if you do slip, they do nothing to stop your slide.
An ice axe, in addition to being a handy source of stability when walking, will (if employed properly), help stop you sliding if you lost your footing. If you want to know what to google, 'self-arrest' is the skill of using an ice axe to stop a slide.
The two should work together, in combination with the knowledge of how to use them.