There is a grain of truth in that it is an advantage running off AC, instead of battery. Generally, you start to see AC-powered bluetooth speakers as you reach a higher level of sonic performance. An example is here: http://www.innerfidelity.com/content/peachtree-audio-deepblue2-table-top-bluetooth-speaker. That is a $449 speaker that runs off AC only.
So, you will have to pick -- if you want better sound, probably AC only; want portability with battery, you may need to compromise on the sonic performance.
So, you will have to pick -- if you want better sound, probably AC only; want portability with battery, you may need to compromise on the sonic performance.