With decreasing costs of high-throughput sequencing, more and more studies have started to provide multi-omics molecular profiles of cancer patients. This has led to various developments of novel survival analysis approaches integrating these heterogeneous molecular and clinical groups of variables. While some of these methods have reached state-of-the-art results in cancer survival prediction, many have demonstrated a decay in performance when integrating larger numbers of omics modalities. Here, we address the need to review and further investigate this decay shown by multi-omics integration methods, i.e., assess their modality-level noise resistance. Concretely, we compared eight deep learning and four statistical integration techniques for multi-omics survival data on 17 datasets from The Cancer Genome Atlas (TCGA) in terms of their modality-level noise resistance and general performance. We found that one neural network method, late fusion using the arithmetic mean, and two statistical methods, PriorityLasso and BlockForest, performed best in terms of both noise resistance and overall discriminative and calibration performance. Nevertheless, all tested techniques struggled to adequately handle noise in the form of a high number of modalities and decreased in performance when less informative modalities were added during training. In summary, we confirmed that current multi-omics survival methods are not sufficiently noise-resistant. We recommend relying on only modalities for which there is known predictive value for a particular cancer type until models that have stronger noise-resistance properties are developed. All of our results and code are available at https://github.com/BoevaLab/Multi-omics-noise-resistance.