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.
Well I own the UD3H (I am using it right now), so I might be a little biased.
The reason I would recommend the UD3H over the UD3R is that if somethign goes wrong with your graphics card, at least you don't need to have another one on hand, because the motherboard can utilize the on-die graphics from the processor in order to find out what the problem is.
According to Gigabyte's website the UD3H (and the UD3R) can support up to 2133 MHz. What you should be focusing on is what the processor can handle.
Intel lists the i5-2500k and the i7-2600k (and pretty much any i3/i5/i7) as supporting up to 1333Mhz.
There must be a workaround for this, which may include some kind of overclocking, but I am not really sure how that works. You might want to open a thread in the CPU & Components section, and ask about how to utilize memory speeds higher than 1333MHz on 2nd generation core ix-xxxx processors.
Once again, for reasons I already stated, I would recommend the UD3H. And once again, I'm probably biased because I own one.
@jsanthara - gave good insight to each MOBO and the differences.
I assume you're adding a Discrete GPU and if you have no reason to encode MPEG-2/4 then LucidLogix Virtu is more a headache than an asset.
If you plan to run 2133 MHz then know you'll need to manually set the DRAM Frequency, CAS Timings, DRAM Voltage and probably the QPI/VTT/VCCIO Voltage. IF running as 4X4GB then it's more miss than hit to keep your DDR3 2133 running per spec and may only run at DDR3 1600 speed.
IF your need is gaming IMO i5-2500K, F3-12800CL8D-8GBXM or F3-12800CL7D-8GBXH with the GA-Z68X-UD3R-B3.