Heat 3 tablespoons extra-virgin olive oil in heavy large skillet over medium heat. Add onions; saute until tender, about 5 minutes. Add garlic; sauté until golden, about 3 minutes. Stir in tomatoes, basil, and capers. Simmer uncovered until mixture thickens, stirring occasionally, about 15 minutes.
Meanwhile, heat remaining 3 tablespoons oil in another heavy large skillet over medium heat. Sprinkle fish with salt and pepper. Add fish to skillet and cook until light brown at edges but pink in center, about 3 minutes per side.
Pour in tomato mixture. Simmer until fish is opaque in center, about 5 minutes longer. Serve fish immediately.