The key difference between witch hazel and hydrogen peroxide is that the witch hazel is a medicinal plant which is safe to use whereas the hydrogen peroxide is a chemical compound which is unsafe to use.
Witch hazel is a medicinal plant. Therefore, it has many important uses. More importantly, we can use the extract of this plant as a substitute for hydrogen peroxide. Since hydrogen peroxide is chemical based, it is unsafe for our skin. Therefore, the extract from witch hazel is a better substitute since it is plant based; thus safe.