Difference between V+着+V and 一边+V+一边+V
Off the top of my head, the emphasis appears to be different in these two forms. If I use verb1 + 着 + [verb1 complement] + verb2 + [verb2 complement], the second verb is to me a more important action. For example, I would interpret 你不应该听着音乐做功课 as "You mustn't listen to music while doing homework" and 你不应该做着功课听音乐 as "You mustn't do homework while listening to music". These are not the same. If I want to tell someone that to focus on her homework, I use the first sentence. If I want someone to focus on the music we are listening to (so as to better appreciate it), I would use the second sentence.

In comparison, if I use 一边 + verb1 + 一边 + verb2, there is less of an implicit emphasis on either action. If I see 你不应该一边等巴士，一边拍照, my interpretation is that it does not matter whether the person addressed stops taking photographs and waits for the bus, or gives up waiting for the bus and takes more photographs.