CB 1.x to CB 2.x is not an upgrade. It is a migration. You need to do a full backup, then clone your site, then install only CB 2.x on your clone to ensure the migration can be successful and so you can know what to expect. See the below video in regards to what to expect.
Once CB it self has been migrated you can begin upgrading your CB plugins. I highly recommend disabling any extension that integrates with CB and also unpublishing any non-core CB plugin for the migration.
Note the package installer may fail for a CB 1.x to CB 2.x migration (we are no longer doing 1.x to 2.x migration testing.. it has been well over a year now folks). So you may need to unpackage the zip you download and install CB directly from within the extensions/packages/ folder of that zip.