Min's assessment of a channeler is very similar to the one she tells us when she sees Birgitte - the only difference is that while channelers often have many things that could possibly happen in different situations in their lifetime, Birgitte has lived multiple lifetimes, so thousands of images sprung up.

IE: A channeler doesn't really "need" to be t'a'veren - there is no real need for the Pattern to weave in protective mechanisms when they can adjust the flows around themselves. The key element differentiating the two seems to be that Heroes earn their status, while channelers are born with a lesser capability. It's almost as if the Heroes earn the abilities that a channeler can learn, but only can use them when the Horn is blown.