With the string, the minus sign applies only to the imaginary part; with the expression '-1j', it applies to the whole complex number (both real and imaginary parts).
I don't see any sensible way to 'fix' the string to complex conversion; indeed, I think any change would make it worse than before. It's a known issue with complex arithmetic that x + 1j*y doesn't give you complex(x, y); the conversions from string and the complex(x, y) form are there to make it possible to carefully create a complex number with known real and imaginary parts.
> For example, in pypy we use the same code for parsing literals and
> converting strings, so you get -0.0 in both cases.
But -1j isn't a literal. It's unary minus applied to a the complex number given by the literal '1j'. Python's code *does* give the same results both for converting strings and parsing literals.