Clearly, I am a fan of large chopping knives. For over 20 years, I have been swinging them with great results. For me, a large well made and designed knife like a khukuri will do more work, faster in my hands than a hatchet sporting a 10-12" handle.
That said, I am a recent axe convert. A GOOD axe, that is. It doesn't have to be a LARGE axe, but it needs to be well made, balanced, thin at the bit, etc. My wife purchased me a Gransfors Bruk Small Forest Axe for father's day, and it will outwork and out-chop even my most faithful of khuks and large blades, and it will do it with precision. I have been floored with what I can do with a 19" axe.
As luck/unluck would have it, a massive chunk of the top of my oak tree came down in the backyard a couple of weeks ago after a huge storm. It was over 15' long and about 9-10" across at the base of the thickest part. Branches of all thickness were growing out of it. Most of them super green. Some very seasoned. Cleaving through two 2" thick green branches 6" apart with a single swing was an unexpected surprise. I was aiming at the first one and went through both. They were freely hanging and just snicked off like they weren't there. For fun, I decided to try out a Cold Steel Bowie I got an accidental deal on. 10" D2 blade. Decent design for a "hard use camp knife". After 6 or 7 strikes that rattled my hand something fierce and listening to the hand guard vibrate and buzz with each strike, I was done. I took apart the whole limb/tree top with the little axe in about an hour and a half and stacked the roughly 400lbs of wood in a pile to be cut down smaller for the fireplace in a couple months.
So while I think a larger blade on a quality knife can outwork a hatchet, I'm a now packing a small axe over a large knife for camping use. A good folder and multi-tool will handle most everything I really need to do. Any larger work will most likely be unexpected. I would rather have a 19" axe lashed to my pack that won't tire me out to use. I'm serious. I love that axe so much it now rests on a stand on the mantle above the fireplace between my wedding photos and pictures of my daughter
I think any collection needs a large quality chopping blade. They have their place. The SRK is way too light for that, though. Much better if you want to baton than chop.