Why would a potential supervisor emphasize kind of doctoral degree? I was talking to a potential PhD supervisor about doing a "PhD" in his institution (in Germany). In several occasions he mentioned in an "emphasizing manner" that they award "Dr. rer. nat." in contrast to other doctoral degrees (like "Dr. phil." / PhD). 
In my environment/institution (also Germany), many have a PhD from universities outside Germany and he is aware of that.

Why would he emphasize that? Are differenct "kinds" of doctoral degrees considered harder to get or more prestigious or something like that?

Note: I had the impression that he was saying "be aware of what you´re getting into, "Dr. rer. nat." is serious business" to exaggerate a little...

The field is CS/maths if that is relevant.
I'm guessing that he has had a number of candidates who were unclear on that from the outset and that he's simply clarifying to make sure there's no confusion prior to your joining the lab. I don't know whether this is likely to affect your long-term career, hopefully someone who knows more about German academics can clarify in the comments.