Contempt of Congress is typically a referral to the US Attorney of the District of Columbia and the US Department of Justice. There is nothing particularly special about a DOJ employee being held in contempt - the only notable feature is that they are typically recused and not allowed to work on their case as a government employee.
Unless Congress uses its inherent contempt powers (which are very serious - it allows them to temporarily imprison those held in contempt), this pawns off the choice to the US Attorney of the District of Columbia and the US Department of Justice.
The US Attorney for the District of Columbia
US attorneys have full power to file charges and bring matters before a grand jury. They technically serve at the leisure of the President under the Department of Justice but there is a strong tradition against the President influencing their decisions (I should note here that some legal scholars argue that an employee of the President cannot be compelled by the legislative branch to take action against the President and that doing so violates the separation of powers). Should they file charges that are upheld in court, the person held in contempt will be imprisoned for 1-12 months and fined $100-$1000.
In the case of the Eric Holder incident, the US Attorney for the District of Columbia declined to file charges (there was some questions about this decision that I'll cover below).
The Department of Justice
The US Attorney for the District of Columbia serves under the Department of Justice which will always maintain a united front because it acts as one body. That means if the US Attorney for the District of Columbia asserts that charges should be filed and the Attorney General (or, if they are recused, the highest ranking official who is not recused) disagrees, that dispute will be settled internally. It may end with the US Attorney resigning.
In the case of the Eric Holder incident, the US Deputy Attorney General sent a letter to the Speaker of the House stating that the DOJ will not be filing charges against Eric Holder because of a specific executive privilege issue relating to the case. This was announced before the US Attorney for the District of Columbia, at the time, Ronald Manchen announced his decision, raising questions about Manchen's independence. That said, Manchen later stated that he concurred with this decision.