Learn Mandarin Grammar: V1 + 着 + (O)+ V2 + (O) vs. 一边 ... 一边:

Verb1 + 着 + (Object)+ Verb2 + (Object) is used to explain two actions happen in the same time to a person. It's essentially the same translations with一边...一边 but the emphases are slightly different.

Examples:  

1a. He is driving while listening to music. (It emphasizes the situation in which the person is listening to music)

他听着音乐开车。

1b. He is listening to music and driving at the same time (He is listening to music while driving, or He is driving while listening to music)

他一边听音乐一边开车。Or 他一边开车一边听音乐。

2a. I like sleeping while listening to music. (It emphasizes the situation in which the person is listening to music)

我喜欢听着音乐睡觉。

b. I like sleeping and listening to music at the same time (I like sleeping while listening to music, or I like listening to music while sleeping) - different meaning

我喜欢一边听音乐一边睡觉。Or 我喜欢一边睡觉一边听音乐。