Neither. The exact arc should be left as an experiment for the reader.
If you just want a fast answer, then it's more like vertical than it's like horizontal.
Verticle jumps are those which result in an increase in altitude, and thus are going in directly opposite direction to whatever gravity is present.
Jumping off a wall as you describe is a horizontal jump - orientation of perspective doesn't affect the orientation of gravitation forces (in most planes of existence, at least).
Which of you is correct?
Both, for different reasons. It's a weird physics thing, and the question lies in which factor supersedes the other in a system that always simplifies down to a binary. We can't know which factor should dominate the equation, because it depends on whatever magic is letting the monk do this in the first place.Which of you is correct?
If you just want a fast answer, then it's more like vertical than it's like horizontal.