In the bluetooth case is it the phone handling the output and the Pi is just acting as a server? Or do you have a bluetooth dongle hooked up to your pi? Once a phone's involved you have all kinds of options, for example, I know my phone works with most USB2 compatible DACs, etc.
Interesting you should make that comparison. I just picked up a BT dongle for the Pi at lunch today.
I was however talking about the iPhone doing the BT part, iPhone paired with a BT receiver/Speaker. It actually works very well this way.
I'll test using BT from the Pi to headphones/Speaker tonight using JRemote for control.
Since it appears 12000mAH is way overkill for a portable Pi, I've picked up a couple of smaller capacity USB power banks to try(2200mAh and 3200mAh), along with a Toshiba 1TB slim 2.5" portable drive.
Agreed, a USB DAC hooked to the pi is probably the easiest thing (and is what I plan to do with mine, either routing to headphones or speakers as needed)
The Pi works great with my portable FiiO E17 DAC/Headphone Amp and with the Desktop FiiO dock too.