Many users have now abandoned using MP3 players to listen to their music on cell phones or tablets. However, there is still a market for MP3 players. The Apple iPod models dominate this market of course. However, there are other competitors producing MP3 players, which are worth considering. This is important if you do not want to tie yourself into using iTunes for your songs.
The sound quality is better on a dedicated MP3 player rather than your smartphone.
Not such an important factor as you would think when looking at MP3 players. Most players come supplied with cheap headphones. The best way to improve the sound quality is to buy better headphones.