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Speckle hinders information in synthetic aperture radar (SAR) images and makes automatic information extraction very difficult. The Bayesian approach allows us to perform the despeckling of an image while preserving its texture and structures. This model-based approach relies on a prior model of the scene. This paper presents an evaluation of two despeckling and texture extraction model-based methods using the two levels of Bayesian inference. The first method uses a Gauss-Markov random field as prior, and the second is based on an auto-binomial model (ABM). Both methods calculate a maximum a posteriori and determine the best model using an evidence maximization algorithm. Our evaluation approach assesses the quality of the image by means of the despeckling and texture extraction qualities. The proposed objective measures are used to quantify the despeckling performances of these methods. The accuracy of modeling and characterization of texture were determined using both supervised and unsupervised classifications, and confusion matrices. Real and simulated SAR data were used during the validation procedure. The results show that both methods enhance the image during the despeckling process. The ABM is superior regarding texture extraction and despeckling for real SAR images.