Background: I am a lay person with some passing interest in the law.
The Supreme Court recently decided Utah v. Strieff, 579 U.S. ___, in which it held that the attenuation exception to the exclusionary rule was satisfied by the discovery of an arrest warrant following an unconstitutional stop. After reading the opinion, and especially Justice Sotomayor's dissent, I went looking for the various ways in which the 4th Amendment is applied in criminal cases. As pointed out by Justice Thomas in his opinion, the exclusionary rule requires that "its deterrence benefits outweigh its substantantial social costs," Hudson v. Michigan, 547 U.S. 586, 591 (2006). As I see it, this prevents the exclusionary rule from being a legal remedy to police misconduct: it seems that simply showing that the evidence was obtained illegally is not sufficient to guarantee suppression, but that the courts can weigh the costs and benefits of individual applications of the exclusionary rule on a case-by-case basis.
Moreover, the correctness of the exclusionary rule itself seems to be a matter of contention among judges: Scalia was a notable opponent of the rule, contending that modern "police forces across the United States take the constitutional rights of citizens seriously," and therefore "it is not credible to assert that internal discipline, which can limit successful careers, will not have a deterrent effect." Hudson, slip op. at 12.
There are statutory provisions for civil suits against the police for violation of these 4th Amendment rights under 18 U.S.C. 1983; however, they are unable (I assume) to overturn convictions obtained by such illegally-obtained evidence. Seeing as such evidence may lead to very severe sentences despite stemming from egregiously unconstitutional police misconduct, I doubt I'm alone in thinking that this is a rather unsatisfactory result for the criminal defendant; even more so considering as damages awarded may easily not be enough to noticeably impact the police department: for instance, I imagine the Department of Justice has quite the fiscal buffer against cases like this. Moreover, simply losing a civil suit does not (as far as I know) guarantee that any police force, no matter how corrupt, will be persuaded to police their use of searches and seizures to what is constitutionally permissible.
So, seeing as the appropriateness of the exclusionary rule is a matter of contention, and civil action seems to be the only other remedy that I could find, what are the prevailing opinions of the legal community as to either's effectiveness as a deterrent? Having a constitutional right mostly applicable in criminal cases have a civil action as its primary set of "teeth", with its procedural dentures becoming more and more limited in scope, seems odd. The 6th Amendment, for instance, allows for the vacation of a conviction based on violations of its guarantees; is the 4th Amendment significantly different in modern American law?
Clarification, as requested: Is there a recognized, fundamental difference between the rights and protections granted by the 4th Amendment and the rights granted by the rest of the Bill of Rights, such that the 4th Amendment's power over criminal proceedings is captured only by a rule which the Supreme Court as described as only "deterrent" in nature?