I thought all the files were shared but it looks like TD3 has taken them all.
In a sense they are. While TD3 will install distinctly from TD2 (it won't upgrade your existing install of TD2 unless you specifically install TD3 in the same folder as TD2, which it does not do by default), they will use the same Data Store. This is the main reason the download page has the big red box with the various warnings, the first being "Take a backup".
The error message you are seeing is because your database has been upgraded to the version 3 format. Version 2 will not understand this format. You'll need to restore a backup of your data so that version 2 will understand the database (and any other files that were changed, if you did indeed load any tournaments or templates
and save them with version 3).
If you didn't follow the instructions and take a backup and you really need access to your database for version 2, email me (support@thetournamentdirector.net) and I'll see what I can do. It might be possible to "downgrade" your database. No promises, though, and I can't downgrade saved tournaments or templates.