stressapptest was developed as a more efficient alternative to memtester. It runs a number of threads with randomized transactions with the intention to get the most test coverage in the least amount of time, and is tunable in terms of time spent testing.
memtester sequentially runs a series of patterns, each designed to find specific problems, and can't easily adjust runtime.
Generally, stressapptest is better at finding errors faster than memtester, finding errors that aren't specifically targeted by memtester, finding stress related errors, and finding intermittent errors. memtester has certain types of patterns that can bring out specific DRAM fault types that aren't well covered by stressapptest. So for best validation, you should run both, for some number of hours each. If you are in a situation where you have limited time, like a manufacturing line, a short stressapptest run is a way to have reasonable confidence memory is reliable.