If a third party is investigating something, they still need to present it to a grand jury in order to proceed with accusation and criminal charges hearings. The third party would act as the investigatory agent and present findings to the jury, which would then decide whether or not to send the case to court for prosecution before judge and jury. Unless this law grants the power to indict based on their findings, they simply do not have this power and would need the grand jury to do so.
On the matter of conflict of interest, I don't see much. The courts and juries operate under the judicial branch of government (interpreting laws), while the police are under the executive branch (enforcing laws). These are separate entities which have no connected power, and therefore no cause for conflict of interest. Furthermore, the jury is selected to be comprised of impartial citizens rather than government officials, reducing the possibility of conflict even more.
The third party investigation law is likely the result of suspicion of problems within the police force itself. Typically, an internal affairs department handles investigation of police officer crimes, and this department is part of the police force (albeit a fairly independent part), creating room for conflict of interest problems. This could lead to the grand jury receiving incomplete or false information when determining if the case should proceed. Again, this fault lies not with the jury, but rather the information they are presented. A third party could provide more objective information.