Process v. Management in IT Support?
Conclusion: For IT support in particular, larger organisations should focus on process because a well-developed process enables strong team management, something that's otherwise simply not possible, no matter how good the manager might be.
This conclusion is best illustrated with an example. Say a Service Desk each day handles only twenty service tickets of types that might be handled poorly. In the absence of an advanced process, their manager will likely have difficulty in finding the time necessary to identify and review even this small number. If they do find time, review will often be hours after the event and so too late to make necessary corrections.
This example covers only half the story though. The second challenge is to ensure workload is handled in the most appropriate order, in part ensuring action triggers, for instance email updates and time-based warnings, aren't missed which might otherwise result in failed service.
To control these difficulties, two corresponding monitors are needed, introduced through process, without which you're largely out-of-touch.
With information provided by the monitors, coupled with good people management and mentorship skills, strong team management is reached because all needs and actions are clearly visible and can therefore be adequately handled.
So, I'd suggest process should take precedence.
With these monitors in place, you'll make a big difference to service provision, where "haphazard" becomes a thing of the past.
The manager, empowered to manage by exception, simply zeros-in on everything still requiring action or improvement, with little time and effort required to do so.
Another reason for "process first" is that as well as enabling managerial capability, a process that provides necessary information will also mean there's reduced need to exercise this capability because teams can have the same enabling information, guiding effective, efficient work activity.
So, the team will always receive the managerial support they need while at the same time minimising reliance on their manager.
To move the process forward further and achieve the third "P" of optimal service delivery - performance - teams will ideally have detailed information on their individual contribution, serving to motivate strong levels of work activity and empower managers to fairly oversee where performance might be coming up short in specific areas.
Overall, an end result of advanced process where managers are in control, might be more managerial involvement from team leaders instead.