Unfortunately, I can reproduce the reversed rotations and translations in the WIP and do not know what the cause is, yet. However I can recommend a workaround, that works for me.
Open the 3Dconnexion Properties application (right click the 3Dx icon in the taskbar)
Ensure that the WIP has 3Dmouse focus.
Press the ‘Advanced Settings Button’
Change the ‘Navigation Mode’ from ‘Target Camera Mode’ to ‘Object Mode’ and back again.
For me both Rhino versions now navigate the same, similar to moving a camera. If you want both to use an examine type navigation, then, with the corresponding version of Rhino with 3DMouse focus, change the navigation mode to ‘Object Mode’.
Reversing the axes in the ‘Speed’ dialog is generally not really a good idea.
I am slightly concerned that ajohnblack says “if I twist the Spacemouse counter clockwise, in Rhino 6, it rotates an object counter clockwise”: the default navigation mode is ‘Target Camera Mode’ so that twisting the cap counter-clockwise should result in the object rotating clockwise.
Hope this helps.