I haven't tested this extensively yet, and I don't have 2 GH5s to do a scientific test of I vs II but I have noticed that the IS on the mark II is exhibiting jerky behaviour with my crane gimbal that I don't get with the mark I.
Even though the mark 1 is atrocious for video use, the dual IS with the GH5 makes it tolerable with the crane for the most part. Sometimes it's still a bit jittery. But with the V2 that I have, I get large and sudden jerks that I never get with the mark 1 (I also