Cut tomatoes and nectarines into large wedges and arrange on a platter. Tear burrata into large chunks and distribute over the top, along with any escaped cream (but not the liquid from fresh mozzarella, if using). Scatter basil and mint over salad.
Whisk together vinegars and oil in a small bowl. Drizzle over salad. Sprinkle with 1/2 tsp. each salt and pepper, and add more to taste if you like.
*Find at farmers' markets.