The major difference between the two motherboards is that the UD3H will support the on-die graphics that come with the 2nd generation Intel core i3/i5/i7, while the UD3R will not.
If you get the UD3R you will NEED a graphics card because there will be no video inputs (VGA, DVI, etc.) on the motherboard.
If you get the UD3H [which has video ports (VGA, DVI-D, HDMI, DisplayPort)] and any 2nd generation Intel core i3/i5/i7 (for example an i3-2100, i5-2500, etc.) then you can use the processor's on-die graphics (Intel HD 2000 or 3000 graphics).
There are a few other minor differences. The UD3H has eSATA and the UD3R had 2 more USB 2.0 ports (14 total) and one more SATA 3Gb/s header (4 total). Besides that they are virtually identical.