With the exception of each keyboard physical design, the switch is going to be the most immediately recognizable difference. All three keyboards use MX series switches by Cherry, quite possibly because it's basically the only company to make them in bulk. However, none of the boards use the same kind of Cherry MX switch.
The Razer BlackWidow Ultimate 2013 uses Cherry MX Blue switches, a very tactile and "clicky" variety. So, while this switch is a bit louder than the others, it does give the board a small bit of extra resistance that kicks in right before complete activation, which is very satisfying.
Logitech opted for the MX Brown switches for its very first enthusiast-tier mechanical keyboard. On paper, Brown switches are slightly quieter and easier to trigger than the Blue variety, but they sacrifice that additional level of user feedback afforded by Razer’s choice. The MX Brown is still a tactile switch, however, so there’s still a bit more resistance at the midpoint.
Lastly, the Gigabyte Osmium utilizes the Cherry MX Red switches. It’s a linear switch, meaning that the force at the beginning and end of each stroke is nearly identical, presenting a pretty big difference between either of today's other two boards.
But switches aren’t the only things that matter. While they are one of the most important considerations when comparing mechanical keyboards, additional features like backlighting, volume control, on-the-fly macro creation, and additional port access can often be the deciding factor in a pricey peripheral purchase. While easy to objectively compare, their level of importance will depend more on any particular user's preferences than most other categories.
Let's begin by taking a closer look at each board, starting with the Gigabyte Aivia Osmium.