Java Mission Control has been open sourced lately. It's a full-fledged profiler which can provide a lot information about a running application. Not only it can show how much memory the particular application is using or how often Java GC is kicking in but it also provides information about network utilization, CPU utilization etc.
What would be the use case when using a Java GC logging feature is more preferable in day-to-day application monitoring?
JMC is a tool for visualizing data.
What you probably mean is Flight Recorder (JFR), which is a feature that is built into the Hotspot JVM that collects diagnostic and profiling data from the OS, JVM and the Java application.
One benefit of GC logs are that they can be printed to standard out, which in some cases are more convenient. The Flight Recorder JEP [1] dicusses logging in the alternative section.
[1] http://openjdk.java.net/jeps/328