Multi-omics data, that is, datasets containing different types of high-dimensional molecular variables (often in addition to classical clinical variables), are increasingly generated for the investigation of various diseases. Nevertheless, questions remain regarding the usefulness of multi-omics data for the prediction of disease outcomes such as survival time. It is also unclear which methods are most appropriate to derive such prediction models. We aim to give some answers to these questions by means of a large-scale benchmark study using real data. Different prediction methods from machine learning and statistics were applied on 18 multi-omics cancer datasets from the database "The Cancer Genome Atlas", containing from 35 to 1,000 observations and from 60,000 to 100,000 variables. The considered outcome was the (censored) survival time. Twelve methods based on boosting, penalized regression and random forest were compared, comprising both methods that do and that do not take the group structure of the omics variables into account. The Kaplan-Meier estimate and a Cox model using only clinical variables were used as reference methods. The methods were compared using several repetitions of 5-fold cross-validation. Uno's C-index and the integrated Brier-score served as performance metrics. The results show that, although multi-omics data can improve the prediction performance, this is not generally the case. Only the method block forest slightly outperformed the Cox model on average over all datasets. Taking into account the multi-omics structure improves the predictive performance and protects variables in low-dimensional groups - especially clinical variables - from not being included in the model. All analyses are reproducible using freely available R code.