I will provide some little experience I have had. I am sure details will differ depending on how the system of two graders are set up.
In the system I experienced it is a custom to have the course responsible plus someone external (in my case even from a different country) do the grading. The grading was completed by having a discussion between the two graders about possible deviations. In the system grades are given as a number between one and six in steps of 0.1, so very detailed.
My experience was actually quite remarkable; it concerned a masters/PhD level course. We were most often within 0.2 of each other except in one case (answer) where one had given a 1 and the other a 6. In that case it turned out the question was ambiguous and could be interpreted in different ways. The grades were basically calculated as the average of both but only after we had discussed the problems/deviations. This is, for example, how we discovered the ambiguous question formulation.
From this, albeit miniscule, experience, I felt that the benefit of having two persons grading is that ambiguities in terms of questions and answers can be sorted out. It is also possible to discuss the apropriateness of the interpretations of answers given by students. The method also provides what I can call "legal certainty" since the grades will be based on two persons view rather than one. Of course the degree to which it is certian depends on the transparency of the process and to what extent the two gradings become official. The point in "my" case is that both graders have to agree so it is not signed by just one person.
As a grader I also appreciated the possibility to discuss the grading and the corrections jointly made were fair and made the process worth while. I would personally like ot see the system used more, but fear it will be difficult from a financial point of view in many universities (-y systems).