Preheat a grill to medium. Brush the bread slices with 2 tablespoons olive oil. In a large bowl, combine the tomatoes, onion and garlic; season with 1/2 teaspoon each salt and pepper. Let stand for 15 minutes. Add the vinegar and remaining 2 tablespoons olive oil.
Meanwhile, arrange the bread on the grill and toast on one side, about 2 minutes. Flip and top with half of the cheese; cover and grill for 2 minutes. Let cool slightly, then cut into cubes and add to the tomato mixture. Stir in the basil.
Pierce the sausages with a fork, arrange on the grill, cover and cook, turning once, until cooked through, about 10 minutes. Thickly slice the sausages and add to the bread salad. Divide among 4 plates and top with the remaining cheese.