In recent years, convolutional neural network (CNN)-based methods have shown remarkable performance in the denoising and reconstruction of super-resolved structured illumination microscopy (SR-SIM) data. Therefore, CNN-based architectures have been the main focus of existing studies. Recently, however, an alternative and highly competitive deep learning architecture, Swin Transformer, has been proposed for image restoration tasks. In this work, we present SwinT-fairSIM, a novel method for restoring SR-SIM images with low signal-to-noise ratio (SNR) based on Swin Transformer. The experimental results show that SwinT-fairSIM outperforms previous CNN-based denoising methods. Furthermore, the generalization capabilities of deep learning methods for image restoration tasks on real fluorescence microscopy data have not been fully explored yet, i.e., the extent to which trained artificial neural networks are limited to specific types of cell structures and noise. Therefore, as a second contribution, we benchmark two types of transfer learning, i.e., direct transfer and fine-tuning, in combination with SwinT-fairSIM and two CNN-based methods for denoising SR-SIM data. Direct transfer does not prove to be a viable strategy, but fine-tuning achieves results comparable to conventional training from scratch while saving computational time and potentially reducing the amount of required training data. As a third contribution, we published four datasets of raw SIM images and already reconstructed SR-SIM images. These datasets cover two types of cell structures, tubulin filaments and vesicle structures. Different noise levels are available for the tubulin filaments. These datasets are structured in such a way that they can be easily used by the research community for research on denoising, super-resolution, and transfer learning strategies.