Ok, now that i had some time i have tried to apply my mesh to the armature. The "nice looking" armature in Blender makes the mesh completely distorted in the asset editor. Only the "strange looking" armature (the one in the screenshot of the initial post) results in a correct mesh in the asset editor.
The problem is that the joints which are connected in the "nice looking" armature are not connected in the "strange" one. They are still in a parent/child relation, but the connection is lost. When i now want to move a bone in the "nice looking" armature the child and parent bones transform accordingly because of the connection of the joints. In the "strange" one this doesn't happen because of the missing connection. This results in faulty meshes in the asset editor.
So the initial problem was "solved" in blender but this solution causes problems in CS. Is there any other advice?
Edit: Or am i wrong and you should not change the armature at all? do i have to change my mesh to fit onto the armature?