Better than you might think, if you only use one or the other. You actually have to crop quite a bit out to destroy the watermark, and it will survive recompression much of the time.
Try this. Open the watermarked image. Rotate it 27.58 degrees counterclockwise. Save the rotated image as a Q75 progressive jpeg file. Open that saved file up. Rotate the image back to original orientation, 27.58 degrees clockwise. Crop back to the original proportions if necessary, and save the result as a Q50 standard optimized jpeg.
Congratulations, you'll just have wiped the Digimarc watermark about 99% of the time. Remember - rotate, compress, rotate back, compress again. The finished product will probably be somewhat softer than the original, but not offensively so most of the time. And actually, I just made up the numbers for how much you should rotate it - it really doesn't matter, so long as it's not a multiple of 90 degrees. ;)