Quake 4 takes place right after the story of Quake II
& you play as a Marine named Corporal Matthew Kane. You join an elite team called Rhino Squad and fight against an alien cyborg race known as the Strogg. Due to the successful efforts of Bitterman in Quake II where he killed the Strogg's leader (The Makron), Earth has been given a chance to launch a full-scale assault on the aliens home planet Stroggos.
This game is very enjoyable if you're into FPS Action games. It does slightly differ from Quake II in terms of gameplay - but keep in mind Quake II released 8 years before Quake 4.
Now, regarding this version (German) difference against the international version, is basically the blood & gore. The game is still in English, so you don't need to worry about understanding German.
Any part of the game that has blood & gore has been tweaked to remove it. This is noticed right away in the intro. As seen in the Quake 4 International Intro:
There is a lifeless half body floating in space, and at the very end of the video (2:49), a marine tries to help you up to which he gets shot and blood splatters everywhere.
Here is the same intro on the German version:
And as seen, there is no lifeless body at the start (2:18), and no blood from the marine being shot (5:07).
So this version is very clean. However, you are missing out on a lot of context with the blood & gore removed. But if you don't like blood & gore, then this version is more for you.
But it is still a great game to play even with no blood & gore, and a great chance to stack the gamerscore again if you already played the international version.
However, the multiplayer achievements are brutal & super time consuming to get, and the multiplayer is completely dead so boosting is the only option. Also, there are some issues to be aware of which can stop you from getting the multiplayer achievements: Leaderboards Not Tracking/Updating for Multiple Xbox 360 Games
I would still recommend playing Quake 4 in general despite the hard achievements, even if you do it on an alt account.