Either a pistol grip stock or a pistol grip only on a Mossberg ergonomically doesn't work well. Because of the location of the safety on the end of the receiver just above where the stock mounts, it's difficult to function with a pistol grip. It requires moving your hand off the grip first. It's not impossible but it takes an extra step opposed to using a traditional stock which means moving just your thumb. A birds head grip may be a little different as the shape, while being a pistol grip, more closely resembles the grip on a traditional stock.
Additionally, a stock allows you to actually shoulder the gun as intended so you can properly aim, something I strongly advocate though I know others depart from my ideollogy on this. Not all, but a few. There are proponents of pistol grip only who may be able to give some more insight.
I honestly can't think of any pros to pistol grip only or a pistol grip stock. I think if you're going to have a stock on a Mossberg it may as well be a traditional styled stock although some companies make recoil reduction stocks that aren't available with anything other than a pistol grip configuration and the same is true with adjustable stocks. In these cases there aren't other choices.
Pistol grip only is easier to store I guess, but that's all I got for it.
