From my experience, C3 felt more C-like(maybe because it has 100% C ABI compatibility) with its context-free grammar and the motive to stay minimal while Zig felt more C++ like due to the OOP-like methods and its ambition to be able to do everything.
This is partly true. But I want to add that the ergonomics of C3 is there to make general app development smooth, whereas for Zig that is not really the focus.
So the goal for C3 is to also be used where you'd use C/C++/Swift/ObjC today.