This study investigates the different performances between Compact-Polarimetric (CP) and Full-Polarimetric (FP) SAR to retrieve multiple crop growth parameters including Vegetation Water Content (VWC), Leaf Area Index (LAI), height, and dry biomass. The objective is to study at which conditions the CP SAR can obtain comparable retrieval accuracy as FP SAR for specific crop types and growth descriptors. Polarimetric decompositions were used to extract CP and FP explanatory variables to quantify crop growth status. Then, the sensitivities of CP and FP variables to different crop descriptors were analyzed, revealing higher sensitivity to height than LAI, VWC, and dry biomass. In order to reduce the information redundancy of sets of CP and FP SAR variables, Partial Least Square (PLS) approach was used to develop new orthogonal SAR parameters, while Step-Wise Regression (SWR) was used to determine the optimal SAR parameters, followed by retrievals of multiple crop growth descriptors using the developed estimators. Validated by the ground measurements, the retrieval performances are found to be highly dependent on polarimetry dimension (CP or FP), crop types, and targeted crop descriptors. With crop growth and enhanced depolarization effects, the CP SAR can capture the increasing volume power and decreasing surface power but at a lower rate than FP SAR. The m-δ and m-χ decompositions provide similar scattering components which differ from the Random Volume Over Ground (RVOG) decomposition. The third Stokes parameter g3 of the CP SAR data that indicates the strength of the circular polarization component is a common important parameter to infer the multiple crop parameters of interest. In agreement with the sensitivity analysis, better retrieval accuracies were obtained for height and dry biomass than VWC and LAI. For short vegetation such as soybean, full polarimetry is required to obtain the estimates of all four crop growth descriptors. On the contrary, for tall crop growth parameters, such as canola (height and dry biomass), corn (height, VWC, dry biomass), and wheat (LAI, VWC, dry biomass), the CP SAR features can provide comparable robust retrieval accuracy as the FP SAR features. This study deepens our insights into the CP SAR of the RADARSAT Constellation Mission (RCM) to timely monitor crop growth and health status.