Grand Juries and their effectiveness and use vary by state. For instance, in CA a Grand Jury is rarely ever utilized for criminal indictments, but in some other states it can be the chief method of indictment - at least for more serious offenses. Also, out here, they are chiefly used to look into matters of interest within the county where they are empaneled. These can include matters of public interest - possibly corruption - or simply the efficiency of a governmental body. In my state they are not all that pervasive or effective.
I suspect that you will find that their effectiveness, bias, etc. will vary greatly by state and jurisdiction. There is no easy way to ascribe the nebulous concept of "fairness" to any particular grand jury process, much less to grand juries in general. But, for criminal matters you have to consider that a Grand Jury generally only hears that info which the prosecutor wants it to hear; hence the saying that through a grand jury a prosecutor could indict a ham sandwich.
A summary of some of the powers of the Grand Jury in various locales and jurisdictions can be found here:
https://en.wikipedia.org/wiki/Grand_..._United_States

