The UD3H has 2 more SATA III 6Gb/s ports using a Marvell controller in addition to the standard 6 Intel SATA III ports. It also lists more supported RAM speeds, but usually each will support more RAM speeds even if not listed. Sound quality should also be a little better on the UD3H.
Both are good boards with a decent amount of upgrade flexibility. You should also consider an Asus Z87-A board if you're looking for similar specs and not going for extreme overclocks. Not saying Gigabyte boards are bad by any means, they have always outlived their warranty periods for me, but over the years, Asus boards have given me the fewest problems.