having said that i have used the lk35 frame without the sack for porting heavy loads short distances (water carriers etc) but that’s not the same as the scenario you are describing.
i'd suggest it kind of is the same scenario. i do a fair bit if green woodworking of various sorts and that means i am often scavenging windfall and suchlike for my wood supply.
given the choice of taking the LK35 or the Sting out through the bush and hills where there are no trails -- clambering up and down hillsides and through unmanaged woods -- to haul back 30, 40, 50 kilos of wood i'll take the LK35 any day. more stability under weight, better weight distribution, more options for lashing and so forth. IMO it's not that the LK35 in particular is better at this kind of thing (though it is unusually good), i'd say pretty much any well designed external frame pack would offer the same benefits.
on the other hand, for a couple days out where the load is mostly bulk vs dead weight -- especially if there is long hiking on more or less prepared trails -- i'd opt for the Sting. that adjustability is hard to beat for the long haul.
in my experience external frame packs are more adaptable -- i run several different bags on the LK35 frame for instance -- and by far the pack of choice for heavy, difficult loads through difficult terrain. the Sting, or any other internal or frameless pack, not so much.
that said these are just my experiences and preferences. YMMV.