Compton cameras and collimated gamma cameras are competing devices suitable for prompt gamma detection in range verification of particle therapy. In this study, we evaluate the first approach from the point of view of the tomographic reconstruction step by comparing it to the second. We clear any technological constraints by considering a simple geometry, ideal detecting stages, a mono-energetic synthetic phantom. To this end, both analytic (filtered back-projection) and iterative (list-mode maximum likelihood expectation maximization) algorithms are applied in conjunction with total variation denoising. It was shown in previous studies that compared to the mechanically collimated camera, the Compton camera has a higher efficiency. Factors between ten and one hundred were reported. Meanwhile, for each detected event the emission position of the original photon lies on a conical surface for Compton cameras, instead of a line for collimated cameras. This leads to a supplementary degree of freedom that logically calls during image reconstruction for a larger data set and may cancel out the benefits of the superior efficiency. We consider here a static Compton camera and a rotating collimated camera with similar angular coverage. We show empirically that reconstruction from conical projections requires ten times more detected events to obtain at least the same image quality. In some experiments, the Compton camera allows to avoid severe artefacts produced by the limited-angle geometry of the collimated camera. In addition, the Compton camera should be better suited for imaging high-energy and poly-energetic sources.