I tried it out myself in creating a new contact group and moving my contacts around a bit on Google Contacts. I did notice a few things:
- For a new contact created through the Google Contacts interface (not linked to any Google+) account, you can only group it into the Google Contact groups and not into the Google+ circles。
- For a contact via your Google+ circles, you still have the option to put them into the respective Google Contacts group.
This means that a Google Contacts group can have a mix of the two types of contacts. However, Google+ circles can only contain people from Google+ and not people that you have add through the "New contact" form in Google Contacts. As for the difference, I can only say that it is a technical difference (and limitation).
I would suggest keeping to the old Google Contacts groups as there is some use of it if you synced the contacts to your Android phone. It makes it easier for you to find your contacts using a custom group that you might have created using it and even add new contacts that do not have an account on Google+.
The Google+ circles are mainly for use by Google+ and possibly Gmail, but the groupings doesn't really have any effect, it only changes how you "group your friends".