Actually, it's not exactly two investigations. In criminal cases, if you face at least 10 years in jail, the investigation is not headed by the prosecution or the police, it's a special judge, who's actually a sitting independent judge. And his job is to head an investigation, seeking both proofs for you or against you (with the help of the police, who executes his orders and requests), and then presenting everything to the prosecution and the defense lawyers before going into trial. So because his job is not to convict you, like the prosecution, his investigation is actually much more neutral, with some exceptions.
It's quite a good system in theory, but it has some quirks.
It's quite a good system in theory, but it has some quirks.