Thanks for reporting, it can be hard to know when mixing different hardware and drivers will lead to trouble, particularly for large datasets where hardware limits might come into play. In this case it might be the dimensions of the volumes - maybe volumes that pass certain sizes in one dimension lead to this kind of issue.
Slicer delegates volume rendering to VTK, so the best way to document and perhaps fix these issues is to supply pure-VTK scripts and sample data the VTK developers with information about how to replicate the issues (exactly which card/driver combinations lead to the issues). See this thread for a somewhat similar issue. The issues may be fixable or they may at least be detectable so the user is warned of possible failure modes.
In the mean time, probably best is to use the CropVolume module to either resize or subset the volume of interest so that it can be rendered on the available hardware.