Axe or Machete?

I want to put either a machete or an axe in my BOB. On one hand a machete is good for trail clearing and small trees for firewood and shelter. not to mention the removal of the head of any zombie that may wander my way. On the otherhand, an small axe will chop wood and with a flattened head will hammer nails. I dont know which I will choose. Maybe both, but then weight becomes an issue.