hy hacker-de-luxe seems to be a grip-issue on the 2nd chuck ... seems promising that same operation performs nice on the okuma, but comparing an identical setup that runs on 2 different machines involves a few things, and, for that, i need to 'see' the machines
considering that you compare a swisstype with a turrettype, i would 1st look into clamping travel of the swiss, being sure that all parts are being clamped somewhere in the middle of the travel :
... let's say that part dia is 10
... check what diameter can enter inside the collet when it is:
...... fully opened ( no part inside it )
...... fully clossed ( again, no part insid it )
* you will need a set of rods, like 9 9.1 9.2 9.3 .... 10.5 10.6 10.7, thus it requires an incremental rods set, with the increment equal to an accuracy that suits your setup
for example, if the collet chuck clamp range can handle:
... 9 - 11, and all your parts are between 9.98 and 10.02 ( 0.04 variations is huge for a swiss, but whatever ), then the only issue may be contact area and/or clamping force
... 9.9 - 10.3, and all your parts are between 9.95 and 10.1, then you are too close to the limit ( = grip instability ); should i explain more ?
is all about tolerances ... swiss machines have a small clamping travel, and that travel may shift depending on a few things, like how much you tighten the spindle nut, and others
i would 1st check that part-clamping range is fully contained within real-collet-clamping range, considering machining tolerance, etc
on bigger swiss machines, available range increases, thus there are lower chances for a missgrip ... on smaller swiss machines, chances for a missgrip are higher
so, check how far are you from the available range limits / kindly