What is the difference between power metal and death metal?
To make my confusion clearer:
I'm just getting into heavy metal and have a rather thin collection of metal albums (Prolly less than 20). One of my favorites (and most recent addition) has been Amon Amarth - With Oden on Our Side. I initially thought that the album was power metal until I saw it referred to as death metal. I instantly sought out a Nile music video to confirm my suspicion that Amon Amarth sounded nothing like them. I listened to the Nile song, and was pretty content that they were two different genres of metal until I saw Amon Amarth referred to again as a death metal band.
With their melodic style and a sound pleasing to the ear (including a badass breakdown in Gods of War Arise), they are what I'd associate more with power metal, rather than the extreme fast-pace and dissonance I expect from death metal bands like Nile.
Where am I going wrong? What constitutes the difference between the genres?