Despite the rapid progress in speech enhancement (SE) research, improving the intelligibility and perceptual quality of desired speech in noisy environments with interfering speakers remains challenging. This paper attempts to achieve high-fidelity full-band SE and personalized SE (PSE) by modifying the recently proposed band-split RNN (BSRNN) model. To reduce the negative impact of unstable high-frequency components in full-band speech recording, we perform bi-directional and uni-directional band-level modeling to low-frequency and high-frequency subbands, respectively. For the PSE task, an additional speaker enrollment module is added to BSRNN to make use of the target speaker information for suppressing the interfering speech. Moreover, we utilize a MetricGAN discriminator (MGD) and a multi-resolution spectrogram discriminator (MRSD) to further improve the human auditory perceptual quality of the enhanced speech. Experimental results show that our system outperforms various top-ranking SE systems, achieves state-of-the-art (SOTA) SE performance on the DNS-2020 test set, and ranks among the top 3 in the DNS-2023 challenge on the PSE task.