I large survival blade does have more utility and may even weigh the same or less, though for wood processing it may be a pain. Then again, depending on where you are, you may just be able to use smaller wood laying around versus going Paul Bunyan on a tree.
In all honesty, a small Gerber fiberglass hatchet or a Fiskers one with the same handle don't weigh all that much. From experience, a short hatchet is a pain to use for chopping wood, though much better than a large knife. Hatchets are pretty cheap too for a good one, $30 or so. A good knife for chopping may be $100 or so. Get a hatchet and give it a go.