Is it better to create parent groups, or a parent group with sub-groups underneath it? Is there a difference?

Depending on whether the surveys are specific to a particular company and you are managing several surveys for them on your site, it might be worth distinguishing that group from the others. In that case, creating a parent category and sub-categories could be useful for navigating the hierarchy of participants or for keeping track of the chronology of surveys.

If you are using IRIS as a survey tool on your website and it is intended solely for your customers and staff within your company or organisation, then you can create just one parent category (for example, ‘Employees’ could be an overarching category covering ALL surveys intended for employees, whilst ‘Customers’ could be a second parent category intended for your customers).
A categorisation scheme with sub-categories could also be considered.

It all depends on how you work, and what works best for you and allows you to develop.