Possible complement of $L =\{a^n b^{n+1} : n\geq0 \}$
Once we've fixed the alphabet, the complement is simply the set of all strings over that alphabet that don't have the form $a^nb^{n+1}$. Presumably, here, the alphabet is $\{a,b\}$.  Again, once the alphabet is fixed, there is only one complement.  You've given two and it's unclear whether you mean "I'm not sure which of these answers is right" or "It's the set of all strings that are either like this or like that."

In fact, neither of your two answers is correct. The complement also includes the string $abbb$, even though it has more $b$s than $a$s.