Crop identification at the field level using remote sensing data is a very important task. However, the use of multispectral data for the construction of vegetation indices is sometimes impossible or limited. For such situations, solutions based on the use of time series of synthetic aperture radar (SAR) indices are promising, eliminating the problems associated with cloudiness and providing an assessment of crop development characteristics during the growing season. We evaluated the use of time series of synthetic aperture radar (SAR) indices to characterize crop development during the growing season. The use of SAR imagery for crop identification addresses issues related to cloudiness. Therefore, it is important to choose the SAR index that is the most stable and has the lowest spatial variability throughout the growing season while being comparable to the normalized difference vegetation index (NDVI). The presented work is devoted to the study of these issues. In this study, the spatial variabilities of different SAR indices time series were compared for a single region for the first time to identify the most stable index for use in precision agriculture, including the in-field heterogeneity of crop sites, crop rotation control, mapping, and other tasks in various agricultural areas. Seventeen Sentinel-1B images of the southern part of the Khabarovsk Territory in the Russian Far East at a spatial resolution of 20 m and temporal resolution of 12 days for the period between 14 April 2021 and 1 November 2021 were obtained and processed to generate vertical–horizontal/vertical–vertical polarization (VH/VV), radar vegetation index (RVI), and dual polarimetric radar vegetation index (DpRVI) time series. NDVI time series were constructed from multispectral Sentinel-2 images using a cloud cover mask. The characteristics of time series maximums were calculated for different types of crops: soybean, oat, buckwheat, and timothy grass. The DpRVI index exhibited the highest stability, with coefficients of variation of the time series that were significantly lower than those for RVI and VH/VV. The main characteristics of the SAR and NDVI time series—the maximum values, the dates of the maximum values, and the variability of these indices—were compared. The variabilities of the maximum values and dates of maximum values for DpRVI were lower than for RVI and VH/VV, whereas the variabilities of the maximum values and the dates of maximum values were comparable for DpRVI and NDVI. On the basis of the DpRVI index, classifications were carried out using seven machine learning methods (fine tree, quadratic discriminant, Gaussian naïve Bayes, fine k nearest neighbors or KNN, random under-sampling boosting or RUSBoost, random forest, and support vector machine) for experimental sites covering a total area of 1009.8 ha. The quadratic discriminant method yielded the best results, with a pixel classification accuracy of approximately 82% and a kappa value of 0.67. Overall, 90% of soybean, 74.1% of oat, 68.9% of buckwheat, and 57.6% of timothy grass pixels were correctly classified. At the field level, 94% of the fields included in the test dataset were correctly classified. The paper results show that the DpRVI can be used in cases where the NDVI is limited, allowing for the monitoring of phenological development and crop mapping. The research results can be used in the south of Khabarovsk Territory and in neighboring territories.