Is synchronizing of indexed items enabled on both computers (see options of sync location in Preferences > Sync)? In addition, in which folder are the indexed items located?
If the folder is in Dropbox, is the local Dropbox folder in the same relative location on both machines?
If you are indexing folders in your local Dropbox folder, the location of that Dropbox folder must be in the same relative location. We strongly advise leaving it at the default location Dropbox suggests. The default location is in the Home directory, ~/Dropbox.