Does Process innovation lead technology innovation or vice versa

The thought occurred to me in the context of shared services models that are pretty popular in most large multi-business companies in the process of evaluating an upgrade to our ERP package. My company implemented a shared services model years ago and then dissolved it because the ineffectiveness of the ERP softwares ability to handle the org structure and process in a simple manner.

Years later the same SW provider released a new version whose primary benefit is that it enables distributed multi-business organizations to create shared service centers and the financial accounting and back office services that are much simpler to operate and create. This lead me to thinking about the lag between what most businesses were doing and the ability of software providers to deliver the functionality. Centers of Excellence/Shared Services organizations have been around for over a decade but the SW is finally catching up to it.

Then on the flip side distributed computing enabled creation of "offshore" business models and shared services centers as people didn't have to be local to provide the back office support necessary to run daily operations. In this case the technology really led the business process innovation.

So my question remains does process innovation preceed or lag technology innovation. As with all MBA type questions the answer quite confidently can be "it depends"