Preheat oven to 375°F. Whisk oil, vinegar and garlic in small bowl to blend. Season dressing generously with salt and pepper.
Arrange beets in single layer in 13x9x2-inch baking dish; add 1 cup water. Cover; bake until beets are tender when pierced with knife, about 1 hour 10 minutes. Peel beets while warm. Cut beets in half and slice thinly. Transfer to large bowl. Mix in capers and 1/4 cup dressing. Season with salt and pepper.
Transfer greens, with some water still clinging to leaves, to large pot. Stir over high heat until just wilted but still bright green, about 4 minutes. Drain greens; squeeze out excess moisture. Cool; chop coarsely.
Transfer greens to medium bowl. Toss with enough dressing to coat. Season to taste with salt and pepper
Arrange beets in center of platter. Surround with greens; sprinkle with feta. Drizzle with any remaining dressing.