There is a .dropbox folder in the HOME folder (whatever that is set to). It contains the following files:

    $ file *
    config.db:     SQLite 3.x database
    config.dbx:    data
    dropbox.pid:   ASCII text, with no line terminators
    filecache.dbx: data
    host.db:       ASCII text
    host.dbx:      ASCII text
    hostkeys:      data
    l:             directory
    photo.dbx:     SysEx File -
    sigstore.dbx:  data
    unlink.db:     data

config.db doesn't contain any interesting information, the directory "l" is empty, and I can't easily get any information out of the other files. It doesn't seem unlikely that all preferences are stored here, though.

Still, running both instances from a non-default HOME seems like sound advice.