If you used either the Dropbox sync or the backup feature, you should be able to get that data back by syncing or restoring from backup.
If not, you may want to know that ExpressInvoice-Mac stores its files in: Macintosh HD/Users/<the user>/Library/Application Support/ExpressInvoice/Shared. (Macintosh HD/User/<the user> is also the folder that appears in Finder as the user name.) -- The Library folder is hidden - to make it visible, open the user folder in finder, then View->Show View Options, and select Show Library Folder.
This location has not changed from the previous version of ExpressInvoice.
If you can find where the old files are located (the data is a bunch of folders containing .dat files), merely copying them into the current EI save folder should do the trick.