We investigated the spatial resolution and quantitative properties of SPECT images reconstructed using filtered-backprojection (FB) and maximum likelihood-expectation maximization (ML-EM) algorithms. We studied ML-EM as a function of iteration number and projector/backprojector (p/bp) model, and FB as a function of filter. To quantify the image resolution for a shift-variant process we defined a local point response function (PRF). To justify the use of the local PRF to quantify resolution for nonlinear ML-EM we tested the regime over which the algorithm behaved linearly with respect to input perturbations. Using Fourier domain analogs of the local PRF we demonstrated that ML-EM with an accurate p/bp can lead to images of better resolution than FB with a Butterworth or Metz filter or ML-EM with a p/bp that does not fully model the imaging process. We also showed that the resolution improves with increasing ML-EM iteration number, and the extent of the improvement depends on the accuracy of the p/bp model. We conclude that the local PRF can be used to characterize spatial resolution in SPECT images, and that ML-EM offers the possibility of superior resolution, particularly if the algorithm contains a good model of the imaging process.