First - congrats on the BK 2. Whole bunch of knife for the money.
To your question, like others have already said, kinda' depends on your location and situation, as far as Axe vs. machete.
If you're in the Amazon hacking through the jungle ... Machete.
If you're in the North West chopping wood ... Forest Axe/Hatchet
You might want to consider a folding saw. Light, compact, and processes wood like crazy. JMHO
Maybe pair up your BK 2 with a Mora or a SAK. (or both)
Best thing to do it try different stuff and see what works for you. Remember, you can always sell a GOOD knife if you don't like it.
This is one of my favorite combos - not much you can't do with these
Corona Folding saw
Husqvarna hatchet
ESSE 4 (BHK Bushcrafter is giving some competiton)
View attachment 228058
When weight isn't an issue I like to bring along a few "friends" too
View attachment 228059
Good luck and stay safe out there.