either one works...
cubic has the advantage of OpenGL has cube-maps and that boxes are
generally really easy to deal with.
generating cube-map textures may require a little bit of special care to
create though, mostly as not all parts of the cube are necessarily the
same distance, which can lead to a slight visible distortion near the
edges and corners (IOW: it is possible to see the inside of the cube if
not done well).
generally this applies to generating a cube-map texture from input where
uniform distance to each point is implied (such as from a spherical
input image, ...).
equirectangular is better for projecting onto a sphere, since the
stretching near the poles will be again collapsed, and within the sphere
all points have approximately the same distance.
hemispheres can also work, where usually a front/back or top/bottom seam
exists (and for each, a circular region is used from the texture).