The watch lathe says "Peerless Made in USA" on the bed. The headstock locates in a v-shaped t-slot on the bed, rather than the front and back edges of the bed. The design is based on Moseley lathes of Elgin, IL, an old company bought out by C&E Marshall of Chicago, I think in the 1930's. There were tens of thousands of these Marshall Peerless lathes sold after WW2, many to GI Bill students of watch repair. Marshall also sold a Moseley version of this lathe, that was a bit more expensive and more rare now.

I have several dozen watch lathes and can usually tell one brand from another if the picture is clear enough.

The Hardinge lathe is a 1950-1960 HLV, with the 5" wide bed. You can tell by the tailstock design.

Larry