Preheat oven to 450 degrees.
Place golden beets on a baking sheet and Chioggia beets on another baking sheet. Drizzle 1 tablespoon olive oil and 2 tablespoons water over each sheet of beets; season with salt and pepper. Cover each baking sheet with aluminum foil and roast beets until tender when pierced with a small knife, 25 to 30 minutes. Remove from oven; let cool.
Using a dry kitchen towel, rub beets to remove skin. Cut beets into 1/2-inch-thick slices. Heat butter in a large skillet over high heat. When butter begins to bubble, add half of the sliced beets in a single layer. Cook until beets begin to brown, about 2 minutes; add vinegar and season with salt and pepper. Gently stir to combine and turn beets using a spatula. Transfer to a warmed plate and repeat process with remaining beet slices.