I carry 4 edged tools: A small light multi-tool, a EDC "tactical" folder (Emerson CQC-13 these days) that I always have with me no matter what, a fixed blade knife (Faullkniven F1, S1, or A1, depending on how "heavy" I am traveling), and a hatchet or axe (again, depending on how heavy I am traveling), or a machete in the tropics.
I guess the fixed blade is the closest thing to a "survival" knife as classically defined. Of the 4 items, the fixed blade is probably the most versatile, and if I could only have one, I guess that would be the best choice. As for battoning or chopping with a knife, that would only be a last resort if I was stupid or unlucky enough to be caught without a hatcet/axe.