Yes, virtually the same. If there is a difference, "emotional wreck" would probably be the worse state to be in. See Miss Courtney's answer.
Although, I would also say that:
A "nervous wreck" can refer to someone who is expressing things other than nervousness. A "nervous wreck" can apply to someone who is "is crying a lot, very depressed, sad, and or acting abnormally due to extreme shock." So, to me, they are virtually the same. The nervous system (nerves) is often applied to the whole emotional state or life of a person.