Sounds like you're really looking at mid-weight Adventure bikes vs lighter dual-sports.
Poly-cylinder bikes are always going to be heavier and more complex to fix trail-side than thumpers, but they've got better road manners.
IMO, if you're just going on gravel roads, any motorcycle is capable of doing that, from R6s, Goldwings, Harleys, R1200GS. It's just that some bikes are better suited for low-traction environments than others. You don't really need long-travel suspension, 21/18 wheels and full-on knobbies for FSRs.
Weight is still the most important consideration, especially if you're going on twisty or hilly gravel roads. Heavier bikes carry more momentum and inertia will make for more pucker moments when you're trying to turn or slow the bike down on loose surfaces. Lighter is better. With most poly-cylinder ADV bikes, you're typically looking at ~450 lbs.
A neutral seating position is what I'd consider the next important factor. The ability to move around on the bike, stand up on the pegs, shift your weight laterally and backwards/forwards will help counter-balance the bike in low-traction surfaces. A standard bike will be better than a sportbike or a cruiser in this regard.
Both the V-Strom and F800GS are fine for this, the Beemer will have better suspension than the Suzi.
Any reason why you're not taking your S1KXR on gravel roads? Some good 90/10 tires instead of the sportbike rubbers and you should be good to go.