I have owned the H1 in 3G and VG10 and currently own the Benchmade Puukko. The Fallkniven is noticeably thicker (0.2"/5mm) than the Benchmade Puukko (.140"/3.556mm). The two knives have other differences, but that is the most significant difference for me. The extra thickness really detracted from the usability of the Fallkniven to the point where I didn't want to use it.
I did review of an H1 in laminated VG-10/420J a while back. It's thick, as noted, and a rather specialized knife. Haven't handled the BM puukko yet but it appears to be better designed for multiple tasks.
You probably decided long ago but I'll add my 2 cents. I have had an F1 for years and have used it extensively. I just got the Benchmade Puukko the other day and haven't used it yet. the BM seems very nice with a comfortable handle. 3V steel is tough stuff. I use the F1 as a general purpose knife, hunting, food prep, wood prep, camping, etc. I can't say that it is the best at any of them but does well in all areas. based on the blade design of the BM I think it would fill the same roll. The BM came very sharp with a high build quality. I am impressed with the knife. For $125 you get a lot of knife especially since its 3V. I have two F1's in VG 10 and they both are great. The VG 10 is pretty easy to keep sharp but you will have to do it more than the BM given that 3V is so tough. 3V isn't stainless but it takes a fair bit before it will start rusting. A little maintenance should take care of that. Just make sure you keep any 3V knife touched up as putting an edge back on one that's really dull is a bit of a bear in the field. Otherwise, choose the one that you like and go for it. They both are great knives. I would also look at the F1 in COS. More $ but may be worth it.
I bought a F1 and immediately returned it because it was uncomfortable to hold in a hammer and saber grip.
I then bought the 200 Puukko. In my opinion, the Puukko is much more comfortable to hold in a hammer or saber grip. However, the flared handle end on the F1 allows for a good 2 finger chopping grip that you don’t get on the Puukko.
I also prefer the leather sheath for the Puukko to the plastic sheath of the Fallkniven. Less rattle and no need to deal with the annoying strap.
The thickness of the blades are substantially different. I never used the F1, but it seemed to be better suited to splitting wood, light chopping, and striking ferry rods. The thinner blade of the Puukko seems better suited to slicing, cutting, and stabbing.