Looking at Amazon, drywall hammers seem to weigh somewhere around a pound to a pound & a half. In comparison the
Gerber Back Paxe II weighs in at a hair over a pound making it similar to, or lighter than a drywall hammer (depending on the model).
Given that, I'd go with the Gerber over a drywall hammer assuming more of an outdoors use (i.e., your examples of tent pegs & chopping tree branches).
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This is the hatchet I normally use for camping (actually, an older model) and I can't say anything bad about it. It does its job as a small hatchet well and is a handy size for the general tasks like hammering in tent pegs. Its also not too heavy to throw in the pack when backpacking (in my opinion at least).