I'm going to recommend the RAT 5. I was quite impressed with it, it won't be as svelt as the Fallkniven, but I like the wide, flatter blade with the flat-ground profile. I don't own the A1, but I have the F1, H1 and S1. My only issue is the handle is a tad small on the mid-sized S1 and I wouldn't prefer that on the larger A1 (asuming the handles are the same size). The Micarta on the RAT 5 is done really well and it's just a more comfortable handle for me. Additionally, my preference is for a choil, which the RAT 5 has; you lose a little blade length, but I like the ability to choke up with the choil.
I don't think you will go wrong with either the A1 or RAT 5. If you can get your hands on either before purchase that would help. Let us know what you decide.
ROCK6