Prioritizing vulnerabilities for handling is a critical process that depends on various factors, including the nature of the institution and the context in which the devices are deployed. Vulnerability #1, which affects the Command Line Interpreter (CLI) of ACME Super Firewall, could allow an attacker to execute arbitrary commands with administrative rights. This type of vulnerability is particularly severe because it could lead to complete system compromise. However, it requires the attacker to be logged in to the device, which adds a layer of difficulty for exploitation.

Vulnerability #2 affects the web-based management interface of ACME Router models 1010 and 1020, allowing an attacker to bypass authorization checks. This vulnerability is also critical as it can lead to unauthorized access to sensitive information and system configuration. Unlike Vulnerability #1, it does not require the attacker to be logged in, making it easier to exploit.

The prioritization of these vulnerabilities would depend on the specific deployment scenario of the institution. For example, an institution that heavily relies on remote management of devices may prioritize Vulnerability #2 higher due to its remote exploitability. Conversely, an institution with strict access controls and limited remote access might prioritize Vulnerability #1 due to the potential for internal threats.