Man is this a complicated question that is pretty tough to explain in a few sentences.

In short, DNA differs from wild to hatchery fish from the loss of diversification of alleles (I believe this is named 'outbreeding depression'). The chromo counts are identical, and probably 99% of the genetic code is too, it is what is left in the tiny details that determine the differences.

While the environmental factors in raising hatch fish do affect its behavior, the real problem arrises by the numbers of fish being so closely related by the genetic soup method of cultivation. Anytime that the natural selection process is interfered with, there is a strong possibility that natural evolotionary tendencies are being altered which could lead to severe limitations towards long term survival.

William