I've used the AG Large Fat Bag for a few years also and this is the first time I'm hearing of the Big Fat Ass Bag, that thing looks almost perfect. For me, the Large Fat Bag worked pretty good in the firing knee up kneeling position to fill that void under the arm and it makes a pretty good seat too. That being said, I've never really worked out a good way to attach it to my body and I've tried various slings, carabiner, and bungee configurations that left a good bit to be desired. The elastic straps are also pretty much useless to me, I think I used them once. The size of the LFB also didn't really work for me when I tried to use it to pad under my chest in a modified prone (shooting from a vehicle) or if I wedged it between my legs for more stability in a double kneeling position (how I shoot lower rungs of a cattle gate for example).
I might pick a BAFB for the bigger size and integral shoulder strap, which seems like it'd solve a few of my issues with the LFB. My vote goes for picking up the BAFB.