I have picked and eaten mulberries since I was a kid. Those have all been dark purple when fully ripe, and the trees have two different shapes on one tree. One shape is about like you posted, and the other is lobed. Every one of them has been VERY sweet. The only problems I know of with mulberries is the mess that fallen berries can make on a driveway or sidewalk, the stems that go all the way through them and the difficulty getting to them while they are still in the big trees.
WA