Earth observation-based burned area mapping is critical for evaluating the impact of wildfires on ecosystems. Optical satellite data from Landsat and Sentinel-2 are often used to map burned areas. However, they suffer from interference caused by clouds and smoke. Capable of penetrating through clouds and smoke, synthetic aperture radar (SAR) at C- and L-band is also widely used for burned area mapping. With a longer wavelength than C-band SAR, L-band SAR is more sensitive to trunks and branches. Conversely, C-band SAR is sensitive to tree canopy leaves. Thus, the wavelength differences between the two types of sensors result in varying abilities to detect burned areas with different burn severities, as different burn severities cause structural changes in the forests. This research compares ALOS Phased-Array L-band Synthetic Aperture Radar-2 to Sentinel-1 C-band SAR for mapping burned areas across low, medium, and high burn severities. Moreover, a deep-learning-based workflow is utilized to segment burned area maps from both C-band and L-band images. ConvNet-based and transformer-based segmentation models are trained and tested on global wildfires in broadleaf and needle-leaf forests. The results indicate that L-band data show higher backscatter changes compared to C-band data for low and medium severity. In addition, the segmentation models with L-band data as input achieve higher F1 (0.840) and IoU (0.729) scores than models with C-band data (0.757, 0.630). Finally, the ablation study tested different combinations of input bands and the effectiveness of total-variation loss. The study highlights the importance of SAR Log-ratio images as input and demonstrates that total-variation loss can reduce the noise in SAR images and improve segmentation accuracy.