When do randomization methods outshine classical and non-parametric test In which situations is it advantageous to use resampling methods as opposed to classical tests (if the data fit a certain distribution) or non-parametric tests?
Is there a dataset/example that can show this situation (for example a dataset with resampling vs. t-test or wilcoxon test)?
 A: Note that the Wilcoxon(-Mann-Whitney) is a permutation test*, but one based on the ranks (which, since the complete set of ranks doesn't change across samples of the same sizes, removes the need for actual resampling), so there you're effectively asking for a comparison between a resampling test and a resampling test.
*(as are many rank-based tests)

In which situations is it advantageous to use resampling methods as opposed to classical tests (if the data fit a certain distribution) or non-parametric tests?

There are two main considerations with hypothesis tests: 
1) Is the actual Type I error rate close to what we want? 
2) What's the power like under some sequence of alternatives?

Is there a dataset/example that can show this situation (for example a dataset with resampling vs. t-test or wilcoxon test)?

The problem with a single data set is you don't know what the right answers are. Simulation is usually more for valuable illustrating better performance.
So this suggests a simulation study - across a range of situations - to discover where some particular resampling method with some particular test statistic might do better or worse than a t-test or a Wilcoxon-Mann-Whitney.
