I must say that I like the Fenix L1P better. I prefer the form factor with constant diameter and tail cap switch to the twistie action of the Amilite, plus I like to carry my L1P in its holster and haven't figured out a comfy and convenient way to carry the Amilite - it's too big to be comfy loose in my pocket, and it's hard to deply quickly, especially with the twistie switch. The Amilite is brighter, has a bigger hotspot and brighter spill beam, and is a little shorter in length, but the L1P is cooler any day.
If ever get a tail cap switch and a holster for the Amilite I might change my mind...