An initiator might be set up to run jobs in classes A,B,C,1,2.
If you purge the initiator then no job can run in those classes. Whereas if you hold the queue for class C, then the initiator is still available for classes A,B,1,2.
However if you hold all classes then you will end up with the same effect as purging the initiator's, i.e. no jobs will run.
It's many years since I've operatored but I'd purge the initiators as it's easy to identify, in my view, why jobs aren't running.