Iterative methods for the reconstruction of positron emission tomography images can produce results superior to filtered backprojection (FBP) due to their ability to explicitly model the Poisson statistics of photon pair coincidence detection. Many conventional implementations of these methods use simple forward and backward projection schemes based on computing the area of intersection of detection tubes with each voxel. Other important physical system factors, such as depth-dependent geometric sensitivity and spatially variant detector pair resolution are often ignored. One goal of this work is to examine the effect of a more accurate system model on iterative algorithm performance. A second factor that limits the performance of an iterative algorithm is the chosen objective function and the manner in which it is optimized. In this paper, performance of the following image reconstruction methods is evaluated: FBP, ordered subsets expectation maximization (OSEM) algorithm, and maximum a posteriori (MAP) estimation using Gibbs prior with convex potential functions. Using the contrast recovery coefficient (CRC) as a performance measure, this paper presents a lesion detection experiment based on an anthropomorphic thoracic phantom and demonstrates how the choices of reconstruction algorithm and projection matrix affect reconstruction accuracy. Plots of CRC versus background variance were generated by varying cut-off frequency in FBP, post-smoothing Gaussian kernel in OSEM, and smoothing hyper-parameter in MAP. The results of these studies show that all of the iterative methods evaluated produce superior CRCs than FBP at matched background variation. In addition, there is also considerable variation in performance within the class of statistical iterative methods depending on the choice of projection matrix and reconstruction algorithm.