What are the benefits of having a rank based cut-off over a marks based cut-off in entrance exams (if any)? There are usually two types of cut-offs in entrance exams that decide who will and who won't be able to attend the particular institution.
They are :

Rank based
Marks based

In a rank based cut-off system, students with a rank above a specified rank can attend the institution.
In a marks based cut-off system, students who obtain marks above a particular mark can attend the institution.
In my opinion, a marks based cut-off is a much better system since it focuses more on learning, rather than competition.
I also believe that in a rank based system, the focus slowly shifts from learning to being above others. Students start focusing less on actually trying to understand what they need to understand to master a certain topic and more on what constitutes an exam. There comes a point where they no longer make use of their own brain, no longer explore what they're taught and just do what's required to be done for them to clear an exam (say). This is basically what the education system is at most of the places in the world.
Marks based systems are converting to rank based systems at a dramatically high rate.
What would be the benefits of a rank based system over a marks based system (if any)?
When knowledge is measured by an exam, some students will naturally focus more on learning &quot;how to do the exam&quot; instead of the actual content. Others will be more interested by the content. In my opinion, whether the cut-off is rank-based or mark-based has little effect on this. For example, cut-offs for English language exams such as TOEFL are always mark-based, but most exam takers will be happy to practice using old exams. The best way to get students to &quot;learn the content instead of the exam&quot; is to design good exams that can only be passed if one knows the content well.
That aside, the following advantages of each type of cut-off come to mind:
 Rank-based cut-off 
The most obvious advantage of rank-based cut-offs is that the number of students who pass the cut-off is fixed. If this is an entrance exam to some program for which there are limited seats, rank-based is the easiest way to go. It becomes easier to plan resources.
Another advantage of rank-based cut-offs is that they are less dependent on the fluctuations in the difficulty of each year's exam. The exam designers do not have to worry so much about making it &quot;equally difficult&quot; to previous years, because the N best students will pass anyway.
Mark-based cut-off
As you said, the main advantage of mark-based cut-off is that it actually evaluates how well the student knows the content, independently of what their peers know. It is less about competition (which may be good or bad, but that is not the question here) and more about actual knowledge. If the two "logistic" problems discussed above are mitigated (i.e., if the number of seats is unlimited and exams can be designed to be equally difficult every year), then mark-based cut-offs are probably a fairer evaluation of students' skills.