it doesn't appear to me that these are really good comparisons, regardless of which one might prefer. The texture sizes are different on the ground, and there appears to be a front light source showing specular reflection on the Carrara scene, or am I wrong?

Both renderings are decent in their own way, it shows that Carrara is a good renderer, and as you noted a very fast one too, and it also  shows that Bryce is not a bad alternative either, when it comes to rendering with global illumination from a HDRI. But there is sooooo much more to it before doing a comparison of C vs B.

you might want to have the same spaceship rendered standing on a plain grey (50%)  or white ground, no texture on the ground, and making sure there's no lights in the scene, and no ambient component in the rendering or scene, and leave it all only to the GI lighting, with  and another without indirect lighting.  Try one at lowest/fastest parameter settings, and another at highest levels (for nuymber of rays, depth of rays reflections, anti-aliasing and shadow quality etc...