One major difference is that most people, at some financial burden, can choose to change insurance providers whereas in many countries with universal systems (single-payer or otherwise) the government guidelines for what the national service or insurance providers must pay for or not tends to be more consistent across the board.

For instance, this is a struggle for people in many European countries who would benefit from access to specific psychiatric prescriptions which are either not prescribed except after trying various cheaper options or are not even approved because of the potential cost to the government, while the same drug is often available in the US (ranging from $10-hundreds a month, as is typical in the US). Public healthcare in at least California sounds more comparable to the universal single-payer systems I’ve seen in its relative inflexibility.