Supposing that the mesh function is called properly, the syntax seems alright, have you though that they may be coincident?
log(Kmatc0),log(Zmatc0) are the same for both meshes and since you didn't share any actual values it's impossible to tell if vc0_cp1 and vc0_cp0 are the same as well.
Try coloring them differently:
cs1 = mesh(log(Kmatc0),log(Zmatc0),vc0_cp1,'EdgeColor',[1 0 0]) %red
hold on
cs2 = mesh(log(Kmatc0),log(Zmatc0),vc0_cp0,'EdgeColor',[0 0 1]) %blue
Note: if you only see the latter mesh (blue) they are coincident
