There are many options to get portable amps to Europe. I have a Meier Stepdance, had a Meieder Corda MOVE and XXS, I have a iBasso D4 and T5, had a T4. I sometimes use my friend's Fiio E12, I have a Fiio X3, I imported a Soundmagic A10, ...
To answer your question. I have not heard either C5 or C&C BH, but C5 is a class better from what I have read.
From my own experience:
Stepdance is best sounding portable amp I have heard. iBasso T5 is much more portable and is very good as well, but build quality is bad. Fiio E12 is not better to my ears than T5 but more bulky, although with much better build quality but less battery life.
What's your source? JDS C5 will probably be a very good choice nevertheless.