I've got Chichiquelites too, but unlike the Wonderberries they do not seem to naturalize as readily. I get a few, and I also seem to get some hybrids, but eventually they seem to die out.
The Wonderberries not only naturalize, but I've spotted them in other people's yards now. Birds are probably spreading them. For all intents and purposes, I never have to replant them; they just show up on their own now, abundantly. They come close to overwintering but freeze out in our worst extended freezes.
I think they taste about the same. If you notice a difference, you might have "Garden Huckleberries" which are Solanum nigrum. The Wonderberry is stabilized S. villosum x S. guineaensis, and is palatable (if a tad bland) raw. The Chichiquelite is more attractive, having wavy leaf margins glossier fruit. It also happens to have a more open habit, making it much easier to spot the fruit. Sometimes you have to look and feel around under the leaves of the Wonderberry, for the hidden fruit.
Luther Burbank wanted to call Wonderberries "Sunberries", but that is a strange choice for a fruit that is almost jet black. It seems like "Sunberries" should be bright, sunny yellow.