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I've done a comparison of the two motherboards you mentioned and I've managed to glean a few choice nuggets of information which you may find useful.
The Gigabyte GA-Z77X-UD3H is a more mainstream ATX board, compared to the Gigabyte GA-Z77M-D3H, which is a budget mATX board.
The U designation boards feature GIGABYTEs Ultra Durable 4 while D is for boards with Ultra Durable 4 Classic. The main difference between the Classic and non-classic Ultra Durable 4 is the non-classic features 2oz copper PCB's that are supposed to help with heat dissipation.
The UD3H is more versatile when it comes to overclocking. For example the UD3H allows for CPU voltage adjustments, where as the D3H does not. The D3H is capable of some overclocking, but it is limited.
The UD3H will allow you to run either a dual Crossfire or SLI configuration at PCI-E 3.0 x8 speeds. The D3H will only offer you a Crossfire configuration at PCI-E 3.0 x4 speeds.
Given you are building your computer around an i5 3570k, I assume that overclocking is important to you? If it is, and you want to push your processor as far as it can go, then I would say yes, the UD3H is worth the extra investment.