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?

Sword are better, it does one attack damage more while saving one ore. Also there's no evidence that axes break armor more quickly. If you are trying to enchant an axe with Fire Aspect II and Unbreaking III / Sharpness V, then its impossible. You have to get enchanted books and put the enchants on the Axe using an anvil to do that.