What determines which 2 guns you pull out when gunzerking?

Solution 1:

As said, the first and the second weapon are one bundle, and the third and fourth weapons are another bundle. You will start with the bundle where your current equipped weapon is in. When you have equipped your third weapon, the second bundle will be equipped.

Example:

1. Weapon: Shotgun
2. Weapon: Pistol
3. Weapon: Sniper rifle
4. Weapon: Rocket launcher

You've got equipped your rocket launcher and activate gunzerking you'll take your sniper rifle and you'll have your sniper rifle and your rocket launcher equipped. If you’ve got equipped your shotgun, you’ll take the pistol as second weapon. You can change your weapon bundle like you change the weapons without gunzerking, as far as I know it’s impossible to just change just one weapon when you have all the 4 weapons slots equipped.

Using the PC version at least, you can press two number keys, like 1 then 3, you will equip the first gun in your left hand and the second in your right hand (so Right: Shotgun, Left: Sniper, in this case). I don't know if there's a way to do this on console, though.

Edit 2:

Found some interesting facts on the GearboxSoftware Forum:

From top to bottom in your inventory, weapons 1 and 2 gunzerk with each other, and weapons 3 and 4. If you only have 3 weapons, then the weapon you are holding will stay on the right, equipping the weapon 2 if you're using weapon 1, vice versa, and weapon 1 if you're using weapon 3. Switching weapon will switch your right weapon, but your left weapon won't switch.

Solution 2:

The first two slots of your "equipped" guns will be the first set of gunzerking guns, and the third and fourth slots will be the second set. When you start gunzerking you'll be using the first set, but you can switch to the second using the weapon switch button/key.

I saw this on one of the in-game loading screens, but here's a reference from the Gearbox forums.