They are completely identical, save for the display outputsOne would expect a couple of micro-ATX motherboards to have more than one distinctive feature, that does not apply here.
Only the video ports of the H61M-DS2 DVI and H61M-DS2 HDMI are different, as can be seen from the names.
Other than that, they both have 4-phase VRM, four SATA 3.0 Gbps ports, 6-channel HD audio, Gigabit Ethernet and three PCI Express slots: one full-size PCIe 2.0 x16, plus two PCIe x1.
In addition to the above, Gigabyte implemented dual-UEFI BIOS (one for backup) and the Ultra Durable 4 Classic components (fiber-weave PCB, anti-surge IC, etc.).
Overall, the socket LGA 1155 mainboards (Sandy Bridge- and Ivy Bridge-ready) may be worth more than their price of under $50 / 39-50 Euro. One of them paired with Zotac's low profile GTX 650, or that single-slot GT 640 with three video ports, from MSI, could lead to very good systems.