In small bowl, whisk together oil, balsamic vinegar, red wine vinegar, tarragon, 1/4 teaspoon salt, 1/4 teaspoon pepper, and garlic.
Place half the tomato slices and half of the onion slices in a shallow baking dish; drizzle with half of the olive oil mixture. Add remaining tomato and onion slices; drizzle with remaining olive oil. Let stand at least 2 hours, spooning juices over tomato and onion 4 or 5 times.
To assemble sandwiches: Split bread loaves and place, cut side up, on a platter; brush cut sides with marinade. Divide tomato and onion mixture among loaves. Top with lettuce and avocado; sprinkle with remaining 1/4 teaspoon salt and 1/4 teaspoon pepper.