my customer still has a 0.9.6 version of ModX running as CMS System. Can I upgrade it the normal way or wouldn't that work? With normal way I mean merging the new modx files into my directories.
If not, do you guys have a good idea how to do that the best?
The "normal" way definitely won't work for a number of reasons -- mainly because the config and database structure is very different for Revolution.
Using that method will make quite a mess of the site. You could do it by installing a fresh version of Revolution, cutting and pasting everything, creating all users from scratch, and then manually attaching the related objects, but it's very complicated and time-consuming.
If you do use GoRevo, I should mention that it hasn't been tested with MODX 2.5.0. I think it will work, but if you want to play it safe, install 2.3.0, import with GoRevo, then use the UpgradeMODX extra to upgrade to 2.4.0, then 2.5.0, then 2.5.1.