Bureaucracies and courts are not that much alike because bureaucracies are more controlled by rules than courts are. This is not to say that courts do not follow rules. The process of a trial is very much rule-bound. However, other aspects of how a court works tend to be much less controlled by rules.
In a bureaucracy, every person is essentially a cog with their own rules that are set out by the rules. They carry out their duties by following the rules. This is not necessarily how courts work. Courts are more like informal working groups because their personnel (at least the judges and the attorneys) see themselves as a group of related professionals. They all have at least some discretion in how they do their work and they see one another as equals in a profession.
What this means is that courts tend to work on less formalized rules. Lawyers who will likely interact with one another time and time again in their careers start to base their interactions more on personal relationships than on rules and procedures. This allows them to be more flexible and more efficient, but it is not consistent with how a bureaucracy would work.