Due to an insufficient amount of image annotation, artificial intelligence in computational histopathology usually relies on fine-tuning pre-trained neural networks. While vanilla fine-tuning has shown to be effective, research on computer vision has recently proposed improved algorithms, promising better accuracy. While initial studies have demonstrated the benefits of these algorithms for medical AI, in particular for radiology, there is no empirical evidence for improved accuracy in histopathology. Therefore, based on the ConvNeXt architecture, our study performs a systematic comparison of nine task adaptation techniques, namely, DELTA, L2-SP, MARS-PGM, Bi-Tuning, BSS, MultiTune, SpotTune, Co-Tuning, and vanilla fine-tuning, on five histopathological classification tasks using eight datasets. The results are based on external testing and statistical validation and reveal a multifaceted picture: some techniques are better suited for histopathology than others, but depending on the classification task, a significant relative improvement in accuracy was observed for five advanced task adaptation techniques over the control method, i.e., vanilla fine-tuning (e.g., Co-Tuning: P(≫) = 0.942, d = 2.623). Furthermore, we studied the classification accuracy for three of the nine methods with respect to the training set size (e.g., Co-Tuning: P(≫) = 0.951, γ = 0.748). Overall, our results show that the performance of advanced task adaptation techniques in histopathology is affected by influencing factors such as the specific classification task or the size of the training dataset.