We present an analysis of the continuous monitoring of a qudit coupled to a cavity using both phase-preserving and phase-sensitive amplification. We construct a stochastic master equation that describes the quantum trajectories of the system, and derive the corresponding Lindblad operators. We find that the measurement backaction causes spiralling in the state coordinates during collapse, which increases as the system levels become less distinguishable. We discuss two examples: a twolevel system, and an N-dimensional system and meter with rotational symmetry in the quadrature space. We also provide a comparison of the effects of phase-preserving and phase-sensitive detection on the master equation, and show that the average behaviour is the same in both cases, but individual trajectories collapse at different rates depending on the measurement axis in the quadrature plane.