Make no mistake: These bills aren't simply unconstitutional, they are anticonstitutional. They would allow for the wholesale elimination of entire websites, domain names, and chunks of the DNS (the underlying structure of the whole Internet), based on nothing more than the "good faith" assertion by a single party that the website is infringing on a copyright of the complainant. The accused doesn't even have to be aware that the complaint has been made.
I'm not kidding.
The Digital Millennium Copyright Act (DMCA), passed in 1998, is a lousy piece of legislation and a very useful lens through which to regard these two new pieces of legislation. Think of all the stories you've read over the past 14 years of people slapping DMCA takedowns of content that they didn't own, just because they didn't like what it had to say. One that comes to mind is Uri Gellar, the popular psychic who performed spoon bending and other tricks on TV in the 1970s. Using a DMCA claim, he had YouTube pull videos of him being humiliated during a 1973 appearance on The Tonight Show with Johnny Carson, when he had no copyright claim to them at all.