Either will do the job, but if you really want a flatter grind than the typical convex of the Fallkiniven you could do a lot worse than consider a Master Hunter by Cold Steel. The MH comes witha flat grind, in a choice of Carbon or San Mai lll blade too. San Mai lll is a laminated blade just like the Fallknivens. This will save you reprofiling an F1 and the knives are very similar in all but grind (The MH is a little bigger but not much)
I've had a MH in Carbon V for a while now and have been happy using it for tasks and situations where my Fallkniven A2 might be considrered a little OTT. It has performed well and I now rarely go out without it.
I recently treated myself to the San Mai lll version to do a comparison with, and then today I was given an F1 as payment for rehandling a guys knife for him with antler ! I'll be giving all 3 knives a good testing and evaluation over the next few months and will hopefully get around to posting a review/comparison on them when I've given them all a fair crack of the whip.