It's certainly not equivalent. "Third-party doctrine" is extremely bad law that ignores the notion of private relationship. The law even recognizes some notions of private conversations (with your lawyer, and with your doctor), but ignores others (with your cloud provider) because the law is older than the cloud and the government loves making power grabs.

Justice Sonia Sotomayor is right to challenge it. I fear that she is one of a narrow generation that is young enough to understand digital technology, and old enough to remember the right to privacy in personal effects.