The advantage of flash mp3 players is that they have no moving parts (they have an embedded memory chip) and are ideal to use while running or exercising. Another advantage is that they are cheaper than hard disk mp3 players.
Also, as long as the memory does not get corrupted, they will never crash. The disadvantage is that flash mp3 players have relatively low memory, but on the other hand they can be upgraded by choosing a larger memory card.
As new models of mp3 players appear all the time, older ones are available at cheaper prices, even for the hard drive mp3 players.
And lastly, research before you buy. Never purchase a gadget on impulse.