According to J. Paul Getty’s diaries, the are 15 mechanical tables similar to this one in existence. I know of nine. Four in North America: 

• there are two at the J. Paul Getty Museum (the focus of this re-creation effort and this one) in Los Angeles,
• one at the Metropolitan Museum of Art in New York City, and 
• one at the National Gallery of Art in Washington, D.C.

In Europe, I’ve read about five more:

• the Musée Cognacq-Jay in Paris has one,
• the one at the Louvre also in Paris,
• another in the Victoria and Albert Museum in London,
• one in Portugal at the Calouste Gulbenkian Museum, and 
• the one I learned about most recently at the Rijks Museum in The Netherlands. 

This leaves six more for me to locate. Please contact me if you know of any others as I would very much like to add them here (not to mention potentially see them for myself)!

What is interesting about these is that they were made in an approximately thirteen year span, from 1750 until Oeben’s death in 1763. Each slightly different from its sisters. The table that is the focus of this re-creation is, as near as I have seen, the only one with a full-length drawer beneath the moveable portions. Also, from what I can discern from the dates attributed by each museum, it is also one of the earliest made. It appears that the later tables’ mechanisms were integrated into a cartridge rather than having to install individual components: guides, drives, etc. My guess is that as his career progressed and more of these tables were produced, he attempted to increase efficiency during the construction process.