I have a few Google Classic Sites and I sympathise with Sharon's fear that their "upgrade" to New Sites could prove destructive. I'm a newcomer to Groups.io but I can mention some features that differentiate them.
Website builder vs Discussion Forum
100 MB vs 1GB free
Tight relationship with many Google products, including free Google Drive 15GB and Photos.
Page templates such as Web page, Announcements, Lists.
Page trees, sub-page listings.
Auto or manual navigation menu design.
Page comments optional.
Page permissions inherited from site or set at page level.
All members of a Google Group can be granted a level of permissions on Site or Page and a level on Drive folder(s) or file.
They are two very different animals.