The main argument that I hear about Sanchin, is the so called "valsalva manuever". For those who might not know what this is, it is how most weightlifters die. You hold your breath as you try and push the weight and you pass out, or if you have a bad heart it can cause your BP to go way up.
Not all Sanchin methods use this type of training. The style of Sanchin I was taught teaches to breath in and tense AS YOU EXHALE and do the dynamic tension parts. You don't hold the breath at any part.
As to the Chinese methods, I have heard it called "Sam Chien" and it comes from the dragon in kung fu. As far as Karate styles that use it, I know of Uechi-Ryu, Goju-Ryu, Isshin-Ryu. I'm not sure of others.
"Hard won, buy easy lost. True karate does not stay where it is not being used."