I can only speak to the BH2 which seems to be the going favorite. It pairs nicely with the C3 keeping the C3 signature, but adding authority, slam, and a richness. It drives my TF10s, HD595s, and my CIEMs plus even my harder to drive LCD2s very well. However, the BH2 is tiny, has 80 hours battery life, and matches the C3 perfectly in size keeping the combo very compact and easily portable.
+1. C3 & BH/BH2 is a wonderful pairing. I haven't tried the C3 with the E11 yet (I should one of these days). I do often use the C3+E12 with open headphones and that sounds awesome, but the sizes are quite mismatched.