And just what "civil rights" would these be? Far as I can see, one of Hillary's biggest faults is her total disrespect for the Constitution and for the Rights guaranteed to The People in the Bill of Rights. Let alone the rest of the Constitution's Amendments... she'd gladly toss the whole thing in the trash. Just like all her ilk.
No, Hillary's biggest fault is that she's one of the lizard people who live in the center of the Earth and have been trying to take over the surface for eons.
Okay, for a less silly answer, both Democrats and Republicans want to strip away various rights because they're assholes more concerned with power than what's best for the country. Trump is a special brand of asshole because he's pandering to Republicans for their support AND brings his own personal awful ideas that don't match up with the Republican stuff. However, the nonsense he could accomplish for his own personal agenda without the backing of Congress is not that big of a concern to me because it can all get fixes without much bother in 4 years when someone else boots him out of the White House (because I'm about 95% certain if he wins this time he won't win a second term). Same goes for the stuff Clinton could accomplish without Congress getting on board with her plans, and I also think she's only in for 4 years if she wins. That's why I care most about Supreme Court nominees: they will have an almost guaranteed lasting impact on the country that cannot be easily reversed.
So, let's take a look at the various rights that each candidate is likely to assault by way of appointing Supreme Court Justices who will make rulings to weaken or remove them. Your mention of the Bill of Rights and other constitutional amendments is a good way to look at it.
First Amendment: Both have said, done, or supported things that indicate possible harm done to freedom of speech and the press. Clinton would probably push for some things that can be called infringements on free exercise of religion, such as not allowing religious business owners to not pay for contraceptives through insurance plans. Trump has also spoken variously of things that discriminate based on religion, specifically Islam, and has proposed (and mostly walked back on, but still) things like closing mosques or barring Muslims from entering the country or compiling registration lists based on religious affiliations, and those are variously violate the free exercise of religion or the "Congress shall make no law respecting an establishment of religion" bit of the text of the amendment.
Second Amendment: Hahaha, yeah, Clinton is big on the anti-guns thing, so anti-gun Supreme Court appointments would be expected.
Fourth Amendment: Both have spoken in support of surveillance measures that violate requirements for search warrants based on probable cause to search for and seize specific things, both would certainly seem primed to find judges to appoint to support this. A lot of Trump's law and order rhetoric has pushed further into this territory as well, and it's really not hard to find a hardass law and order person to throw on the Supreme Court to support it. Oh, also, those mass deportations Trump spoke of would almost require further violations of this amendment because it would require mass warrant-free surveillance to identify illegal residents.
Fifth Amendment: Trump has said he doesn't want to allow "catch and release" for illegal immigrants who are set to face removal proceedings, instead wanting them detained until they're removed. That would violate the due process clause of the Fifth Amendment, so putting any hardcore anti-immigration nominees up for the Supreme Court could lead to the reduction of due process rights (which have been long established as applying to all persons in the country, not just legal residents).
Eighth Amendment: Trump has spoken in support of waterboarding and said he doesn't think it's enough, plus he has spoken of targeting the families of ISIS fighters. This would not necessarily be unconstitutional if only performed on people who are not residents or citizens of the United States, but seeing as he has also spoken of needing to be hard on terrorists at home this is rather troubling. Oh, and this hypothetical harsh treatment and killing of domestic terrorists would also likely violate the due process clause of the Fifth Amendment. This one is not quite so much a Supreme Court concern, but it's possible he'd find judges who would be down with supporting this kind of shit.
Fourteenth Amendment: There's a ton of things I could go over with this one. Trump has spoken in favor of not granting citizenship to children born here if their parents are not legal residents, and that's a violation of Section 1. I've also heard him talk of wanting states to do things that would violate the Constitution (specifically First Amendment by suggesting they infringe religious freedom of Muslims in various ways), so that's another potential Section 1 violation. Again, all of these are positions he would potentially look for in a Supreme Court nominee, though these issues seem unlikely to come into play in such picks so they're only things to consider rather than true worries in my book. There are more serious issues that fall under this amendment though: wanting to mass deport illegal immigrants would require searches by way of racial profiling, and that's a violation of the equal protection clause of this amendment; Trump has also spoken in favor of voter ID laws that are being challenged and knocked down all over the place, and some of those successful arguments have been based on the equal protection clause because of the undue burden they place on certain segments of the population. These two issues are things that I think very well might factor into a Supreme Court appointment.
So uh, I think that should explain why I'm more concerned about potential Trump nominees shitting on the Constitution than potential Clinton nominees. They've also both got concerning positions regarding parts of the main body of the document as well, but similarly they're either both on the same bad page or it's mostly Trump as the only one with the bad position. I have all sorts of problems with Hillary Clinton, don't get me wrong, they're just severe ethical problems and violations of various statutes rather than what appears to be intent to erode the rights enumerated in the Constitution or its amendments. I could also go into details on civil rights granted by major federal statutes that each one would likely try to smash with Supreme Court picks, but I can already tell you that it will end up looking similarly weighted as the above list. The long-term damage is what I care about most in this election of awful versus terrible, so I'll go with the one that seems like they'll do less of that, and that happens to be Clinton.
