I'm guessing the difference between the two is the pin config and not the hotshoe mounting. Which one do I go for?
Either trigger will work.
The hotshoe on the gh4 is the same as on any Nikon/Canon SLR for the purposes of flash triggering. The extra contacts are to support fancy features (like TTL metering, zooming the flash, telling the camera the flash is recharged, etc.) and are not used to actually fire the flashes.
The reason there are two versions is that Nikon/Canon flashes have a "standby" mode for their flashes which will power them down after a certain amount of time to extend battery life. The different versions of the transmitter work with these different systems to allow you to use "standby" mode on your remote flashes. This will not work on your gh4 with either version but it is not a great loss.
This question has a lot more information if you are interested: Manual off-camera flash compatibility with multiple bodies?
Either version will work, but for some micro four-thirds (mft) hotshoes, the Nikon version may be a better fit. There are reports that the Canon version of the RF-603II has slightly longer pins/a thicker plate, and can be very tight on the mft hotshoe, while the Nikon version is easier to put on the camera hotshoe for some mft models. And I'd suspect that the RF-605 is probably using a foot sourced identically to the RF-603 units. In addition, since the pin placement is different from Nikon vs. the mft/Canon/Fuji/Pentax contact placement, you'll also avoid signal crosstalk.
Also be aware that with the RF-605s, you'll only have group control if the flashes you're using are YN-560III, YN-560IV, or YN-685 flashes or you have another RF-605 attached to the flash as a receiver. And you'll only have remote power control if you're using a YN-560TX as your on-camera transmitter and the remote flashes are YN-560III/IV or the YN-685 (i.e., the RF-605s do not give you remote power control).