Ok, I freaked out and did some tests. The barb axe gets 23% against our axe Leane if left unpromoted. Promoting to C1 brings the barbs chances down to 12%, and adding Shock drops it all the way to 4%. So I logged in and gave the two promotions. Shock axes are what we need against Rome anyways.
I also sent this picture to Asterix:
I also sent this picture to Asterix: