'Unix for mission critical roles, Linux not so much' is misleading
While certain types of workload seem to be popularly run on Unix, often things like corporate databases, it would be misleading to characterize the Linux workloads as non mission critical.
Unix seems to be often favoured for database servers, applications servers, and often web servers.
Linux, on the other hand, is very heavily used in firewalls, filter proxies, DNS servers, DHCP servers, IP administration systems, intrusion detection, intrusion prevention, network monitoring, server monitoring, packet capture and analysis systems, FTP, syslog servers and similar infrastructure components. Obviously failures in some of these will be vastly disruptive to delivery of services. These days, scratch an appliance, and you'll find Linux under the hood.
If I had to classify the situation, it would be that Unix is currently strong at the applications level, while Linux is coming to dominate the infrastructure level.