You would sort in memory when your dataset and/or number of clients is large enough that you would need to distribute your dataset over many servers and the overhead of replication with your preferred RDBMS is too high. E.g. large sorts can be reasonably well parallelized (split the dataset into chunks, sort each chunk, and zipper merge the sorted subsets on a machine collecting the result), and similarly caching the dataset on however many app servers you need in order to do sorts often makes it worthwhile even for much smaller datasets.

If you can run everything on one machine, or your RDBMS handles sharing and replication efficiently and easily, then by all means try that first. But you can often beat the pants of RDBMS' for specialized scenarios.