Effective monitoring of agricultural lands requires accurate spatial information about the locations and boundaries of agricultural fields. Through satellite imagery, such information can be mapped on a large scale at a high temporal frequency. Various methods exist in the literature for segmenting agricultural fields from satellite images. Edge-based, region-based, or hybrid segmentation methods are traditional methods that have widely been used for segmenting agricultural fields. Lately, the use of deep neural networks (DNNs) for various tasks in remote sensing has been gaining traction. Therefore, to identify the optimal method for segmenting agricultural fields from satellite images, we evaluated three state-of-the-art DNNs, namely Mask R-CNN, U-Net, and FracTAL ResUNet against the multiresolution segmentation (MRS) algorithm, which is a region-based and a more traditional segmentation method. Given that the DNNs are supervised methods, we used an optimised version of the MRS algorithm based on supervised Bayesian optimisation. Monotemporal Sentinel-2 (S2) images acquired in Lower Saxony, Germany were used in this study. Based on the agricultural parcels declared by farmers within the European Common Agricultural Policy (CAP) framework, the segmentation results of each method were evaluated using the F-score and intersection over union (IoU) metrics. The respective average F-score and IoU obtained by each method are 0.682 and 0.524 for Mask R-CNN, 0.781 and 0.646 for U-Net, 0.808 and 0.683 for FracTAL ResUNet, and 0.805 and 0.678 for the optimised MRS approach. This study shows that DNNs, particularly FracTAL ResUNet, can be effectively used for large-scale segmentation of agricultural fields from satellite images.