Museum director Paul Spitzzeri, who kindly allowed me to view both cartes de visite recently, mentioned to me that, of course, LA had two Mayors during the year 1860 - Damien Marchesseault and Henry Mellus - and that the man in the mystery picture was definitely not Henry Mellus.
However...
Technically, Los Angeles had three Mayors in 1860 - Marchesseault, Mellus, and (after Mellus died in office) Wallace Woodworth, who served as Acting Mayor for two weeks before Marchesseault again assumed the office. Could he be the mystery man?
I have searched in vain for a picture of Wallace Woodworth. (Does anyone out there have a picture of him?)
On seeing the picture on the right, identified as Damien Marchesseault, my mother commented that he resembled her French Canadian grandfather. The mystery mayor on the left doesn't appear to have any French features (although, to be perfectly fair, I am not a forensic anthropologist).
The man on the left can't be Henry Mellus. But, I don't believe he is Damien Marchesseault. Could he be Wallace Woodworth? Hopefully, someone out there has a picture of Woodworth that could either prove or disprove this possibility.