Included scenes are somewhat static: they have the same size as the scene where they are included, so you will usually use the feature to merge (overlay) two scenes.
Groups are parts of a scene. They don't need to occupy the whole scene. They blend with all the other objects in a scene and are more dynamic, if you arrange/resize them. It's also more implicit if you change something in a shared group: you just change your scene, and if the item you change happens to be a part of a shared group, that part in other scenes changes as well like magic.
I see groups as lightweight versions of sharing screen items, if a whole extra scene is not warranted.
Scenes, on the other hand, might be good if you want one template scene with your corporate identity or whatever you intend to show on every single scene. You design your template scene first, then you create your other scenes by first including the template scene, then add the scene-specific content. On the other hand, this will work with groups as well: you design your first scene with everything and group the parts you want to have in every scene. Then create new scenes and add that group first. Then add the additional items outside of that group.
Nested scenes clutter your scene list. If you use nested scenes, you get scenes you never show, although the purpose of a scenes is to show it.
If it comes to technical aspects, the only thing I see that is different is that groups cannot be nested. Their depth is only one level. Every other feature seems to be shared between both.
