Well, the Fallkniven is going to out-cut the other two by an extremely large margin, not because of steel type (or product loyalty on my part

) but due to its superior blade geometry. It is a full-height grind and so while being of a robust spine thickness it still becomes much thinner at the edge shoulder. The other two are both saber grinds, the kabar a flat-saber and the SOG a hollow-saber. Half the width of the blades are full thickness and then plunge at rather extreme angles down to the edge. This kind of design sacrifices cutting ability for strength, so while both can get very sharp, their ability to pass through cutting mediums will be low when compared to the full-height grind. And also in this case, due to its own thick spine/short blade/most robust tang design of the three, the Fallkniven should actually be stronger than either of the others. The Kabar design is classic and the SOG has racey lines but both are designed as "combat" knives, which is one of those hard to define terms when you really look at it, but essentially they're part weapon, part general cutting tool, part tent stake--essentially designed to do a variety of tasks reasonably well, but not really specialized for anything. The Fallkniven is much closer to a pure cutting tool; its cutting ability would be increased even more with a thinner spine but having a military pedigree itself they were going for a somewhat tank-like quality.
Last but not least, the steel in the Fallkniven will likely be superior for your needs. AUS-8 is a fairly tough stainless and 1095 is a good all-arounder but the VG-10 from Fallkniven will hold an edge longer than either in just about all types of cutting, especially the AUS-8. 1095 is actually capable of very extreme edge holding when its hardness is taken into the low 60s, but Kabar uses the same hardness in the short models as it does in the standard combat knife--around 58 HRC if I remember right--which again is a concession in favor of overall toughness and ease of sharpening instead of pure/prolonged cutting ability. It's not that this philosophy has no merit, but given the size and weight of these blades and the types of jobs they're really suited for, you'll appreciate the edge holding in prolonged cutting more than the ability to strike wood or bone without chipping.
If you combine the Fallkniven with a good machete (easily within the $25.00 range) and possibly a fillet knife, I really can't think of much you'd ever have to do in recreational outdoors use that wouldn't be covered. Honestly, that would cover just about all uses, recreational or not. Of course, as a certified knife knut who owns many many MANY times more knives than he needs, I have to smile at my above statement, but hey--it's my hobby. My brother in law collects toy trains, and I can guarantee he has more than he NEEDS, but...
I'm sure others will weigh in here. Let us know what you decide and welcome to Bladeforums.