I have and use both, both are great knives.
The Fallkniven is stainless with a Kraton handle, the BRKT is carbon steel with various handle materials available, my user is black micarta.
The handle material is very much personal preference. I prefer the micarta handle during summer months, but find the grippy Kraton excellent in winter when wearing gloves.
They both perform well for chopping and batoning, but, in my opinion both are a bit large to excel at fileting and skinning, usable, but probably a bit awkward.
I know this doesn't help you choose one or the other, but both are excellent knives that will serve you well for many years.
I'll try to post some photo's later but have to run for now.
EDIT: Add photos. These have been posted previously, appologize for the repitition.
BRKT Bravo 2 Black Micarta
BRKT Bravo 2 Purple Elder Burl
Fallkniven A2
Fallkniven A2 - Batoning
BRKT Bravo 2 - Batoning
Bravo 2, A2 and RC-4
Bravo 2 and A2 side by side
Kevin