There is no set answer as to whether a civil case should be pursued through the state courts versus through the federal courts. Each civil dispute has to be considered on a case-by-case basis. The reason many federal civil statutes are “on the books” to begin with was the perceived failure of individual states to adequately address non-criminal matters, especially with respect to civil rights as discussed in the context of the U.S. history of racial discrimination. Up to the present, whenever an individual member of Congress feels a case of discrimination – at least as perceived by that member of Congress or by some defined group that feels discriminated against – exists and is not being address by the state(s) in which the grievance has taken place, he or she invariably offers legislation intended to “federalize” the act in question. For example, the 1994 Violent Crime Control and Law Enforcement Act (28 U.S.C. 994) and the 2009 Hate Crime Prevention Act (attached to the National Defense Authorization Act of 2010) were both passed specifically in response to concerns among communities (in the case of the latter law, the gay and lesbian community) that normal criminal or civil penalties failed to take into account the especially pernicious nature of crimes that targeted individuals on the basis of their race, ethnicity, religion or sexual orientation.
Similarly, cases of police brutality, which very frequently have a racial overtone, have garnered the attention of national-level politicians who, for both political and substantive reasons, seek to raise the level of attention to a recurring problem by addressing at the federal level despite the fact that state laws already address the issue. Emotions and politics, sometimes appropriately, sometimes not, often play a large role in how civil matters are addressed. Laws like that specified in the question – 42 U.S.C. 1983 – represent important instances, however, of federal intervention when individual states or groups of states (in this case, the American South circa the late 19th Century) fail to address absolute wrongs that are clearly morally in conflict with the spirit of the U.S. Constitution. The Civil Rights Act of 1871, of which 42 U.S.C. 1983 is a part, was passed by Congress in direct response to the enduring legacy of violent racism endemic throughout the South following the Civil War and the failure of Reconstruction. The Ku Klux posed a violent threat to the continued viability of U.S. law in the southern states, and federalizing civil rights, a practice that would need to continue well-into the 20th Century, was deemed necessary if the scourge of institutionalized racism was to be eliminated.
To reiterate, then, whether civil litigation is best handled at the state versus the federal level is entirely dependent upon the nature of the dispute and a determination of whether existing state laws are adequate to address the dispute and whether the record of enforcement of those laws is adequate. Federal civil statutes exist to address perceived weaknesses in state legal systems. Also, federal judges tend to look askance at what they view as trivial matters better addressed at the state level percolating up to their level, barring any overriding political or moral consideration.