Minecraft - Sword or Axe? (Comparing same material)?

Hi! I have been play a server called Cosmic Craft. I see alot of people using an axe… Excluding enchantments, which is better?

Sword or axe?(same material)

Let's put it in another way.

Diamond sword or diamond Axe?

A lot of people say that axes break armour faster but i recently saw a video on Youtube that test how much a diamond sword and diamond axe does damage. It turns out it was the same. There was no damage from the axe that broke the armour faster than the sword. If i remember, the diamond sword and diamond axe broke the armour with the same damage. I don't see why people say axe breaks armour faster… I need proof some where.

Another side question. I want to enchant a diamond axe with Fire Aspect II and Unbreaking III / Sharpness V

Can you tell me the best level for getting these enchantments?

Thank you in advance.

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