In List-mode PET iterative image reconstruction two major approaches exist in order to model the detector response. The detector response can be measured or estimated before the reconstruction and stored in a matrix. This approach has the advantage of being highly faithful with the real detector response but requires a large among of memory to store the huge system response matrix (SRM). The other approach is based on an on-the-fly projector to compute the required parts of the SRM. While existing for multiple decades, the projector approach was limited to over simplistic detector models because of its computation burden. Since the growth of the general-purpose processing on graphics processing units that allows a large computing power in a simple computer, more complex on-the-fly projectors are now possible. We compared the first approach with the on-the-fly approach in terms of image quantitative and qualitative performances as well as reconstruction speed. Results showed that a simplistic on-the-fly projector cannot reach the image quality of a stored SRM but a more accurate on-the-fly projector can surpass the SRM in term of spatial resolution while running faster especially because a GPU implementation can be used.