Thank you very much for the explanation, Harry. Based on the specs I believe the SONYs don't have the mechanical stabilization which might be the reason for the better results.

Although this issue has in fact been discussed a few times I think it's not a problem with modern phones in general. I used Laptimer with the internal camera of a SONY Xperia SP, Xperia Z3 compact and the XZ1 compact, all mounted with a RAM MOUNT XGrip. None of them had a problem with shaky videos. ...

I already reported this issue as part of the v22 beta program. Obvioulsy it was lost. Hope it will be fixed some time, even if it is not the most important feature, but it's a nice one.