Differences between German computer science doctorates The faculties of some German universities offer a choice of doctoral degrees.  For example, Technische Universität Darmstadt's Department of Computer Science allows candidates to apply for either a Doktor-Ingenieur (Dr.-Ing.) or a Doctor rerum naturalium (Dr. rer. nat.).  Candidates choose which degree they want to apply for shortly before they submit and defend their thesis; the only guidance provided is as follows:


  Der Dr.-Ing. wird im allgemeinen auf Grund einer Dissertation
  verliehen, die überwiegend ingenieurwissenschaftliche Erkenntnisse aus
  der Informatik enthält. 
  
  Der Dr. rer. nat. wird im allgemeinen auf Grund einer Dissertation
  verliehen, die überwiegend theoretische wissenschaftliche Erkenntnisse
  aus der Informatik enthält.


Roughly translated:


  The Dr.-Ing. degree is generally awarded on the basis of a thesis that contains predominantly engineering-related findings in computer science.
  
  The Dr. rer. nat. degree is generally awarded on the basis of a thesis that contains predominantly theoretical scientific findings in computer science.


Other German universities may offer yet other degrees.  I know some computer scientists who hold a Dr. phil. (Doktor der Philosophie).

In some cases where the university offers various doctoral degrees, a thesis may meet the criteria for several of them.  (For example, in the TU Darmstadt example, the thesis may contain engineering-related and theorical scientific findings in roughly equal proportions.) In such cases, is there any reason for the candidate to prefer requesting one degree over the other?  Do the various computer science degrees have different standings or reputations?  Will having one or another make it easier or harder to get certain types of jobs in academia or industry, either in Germany or abroad?
In general, the latin title of the degree conferred at a German university is of purely historical relevance (basically, indicating how the original four faculties of the middle ages split into the dozen or more departments of today, which happened in different ways at different universities -- obviously, Computer Science split off of Electrical Engineering in Darmstadt, rather than, say, Mathematics as in Munich); the important information is which department conferred the degree (which differentiates a Dr.rer.nat in Mathematics from one in Physics or Chemistry).

There is, however, one exception: The Dr.-Ing. (Doctorate in Engineering) still has a special place as an indication of the high regard in which German academic engineering is held (mostly, needless to say, within Germany, as well as by those directly influenced by this system, although a hundred years ago this was indeed something special), and is the reason why Darmstadt is offering a choice -- in effect, it's a marketing strategy to get students to enrol by offering them a degree that's perceived as more attractive. (This is also related to the fact that some universities still hand out "Dipl.-Ing." diplomas even though the Bologna process turned every other degree into a Masters.)

As to whether the choice of degree will make a practical difference in finding a job, that's hard to say. My feeling is that it will most likely play a role when transitioning to industry in Germany, where someone with a Dr.-Ing. might be seen as more "hands-on", practical-oriented, than with a Dr.rer.nat. (especially at small or medium-sized companies which might hesitate to hire a purely theoretical PhD). On the German academic job market, on the other hand, the university (and research group) where you got your title would be much more important. Outside Germany, I'd be surprised if many people cared much about the distinction (unless they themselves are the proud holders of a Dr.-Ing., of course...)