I didn't measure them, but it is very obvious that the SAECO and RCBS are a good deal thicker than the Lyman. About an 1/8", I don't know the metric on this
The SAECO and RCBS appear to be quite close in thickness. These observations where with an "old style" Lyman 4 cavity handle set and a RCBS 2 cavity and the SAECO handles which are supposed to handle anything from 1-8 cavity (I've only used 4 cavity with them) So, my hopes have been dashed, as I don't much care for the Lyman 4 cavity handles that I have. I've only got two Lyman 4 cavities, so I'll probably hold off on the new handles. You are most likely correct in thinking the mould handles are made by the same people, as they are identical in the hinge area as well as the handles.
Another queston: Do the Lyman "small" handles for the one cavity moulds also work with the 2 cavity moulds? I purchased several Lyman 1 and 2 cavity moulds off of Ebay over the winter months. I also purchased a set of the handles that I mentioned above. I haven't tried any of the 2 cavity moulds as of yet, I'm hoping I don't need another set of handles. I don't know if the Lyman moulds from today are the same as the older ones I have. The 2-cavity moulds that I have are considerably smaller than either the RCBS or SAECO 2 cavity moulds.