Both (sort of) or neither. Assuming you mean true north rather than compass then you are following a meridian. If you did mean compass then you are following a magnetic meridian, or close to it, depending on deviation. That is certainly not a rhumb line and although the meridian itself is a great circle by JAA (inaccurate) approximations any compass deviation will take you off the great circle anyway.
By the strictest definition the true meridian is not a rhumb line (definition is a line which crosses each meridian at the same angle; a meridian does not cross any other meridian) but by the more usual definition of a constant-bearing line it is. However a meridian is also a 180° arc of a great circle, so flying ture north you are also following a great-circle path.
Does that help?
Send Clowns
Gen Nav Instructor,
BCFT