High quality does not mean the full original quality, right? This is then as before.
At the moment, there are three web interfaces to access your photos:
https://plus.google.com/photos/yourphotos
I would switch to the latest version but the other interfaces still have their advantages too.
E.g. the old Picasa interface provides the best overview of all my albums (I have a lot: 1619), esp when I want to search an older one (they go back to 2004). Also, it has somehow the most compact view with the most details at the same time, like all meta information (sharing, tagged people, GPS, exif, ...). For videos though, the Picasa webinterface is somewhat broken. Also tagging people didn't quite work correctly.
The Google+ interface has the nicest way to tag people. And I think the photo editor is only available here?
The new Photos interface looks like the most modern one, but otherwise seems to have the least amount of features. Tagging people doesn't really work here. The photo editor is much stripped down compared to Google+. Also, it doesn't really show much meta information (no GPS? almost no exif, etc...).