All the exact SPL stuff is a bit over my head. I guess I will say that your 1212BMF will be massively louder than this cab in an absolute sense (based on my experience with the 115L+, but it will sound much thinner down low, and MUCH more goosed in the low mids and upper mids. That's not a bad thing, just depends what you want.
I have not played a Barefaced compact, but have spent time with a couple LDS 3015 (non LF) loaded small 115 boxes made by LDS (beautiful sound). Punchier than the Thunderchild, and MUCH more aggressive/less smooth in the upper mids (I have a clip of one of these 115HO boxes on my iComposition site, which should be somewhat similar to the one way Barefaced 115 Compact). The voicing to me is between your very bright, very low end attenuated, uber mid voiced BMF cab, and the more wide, even, deep, smooth and pure voicing of the Thunderchild. Maximum volume would probably be pretty similar with a full 500 watts going into each cab, although my guess is the Compact would still 'sound' loude due to the mid response.
Again, on this cab (and also all the 12/6's I've played) you have to turn that master volume knob up quite a bit more (the lower SPL thing), but the cab will take it, and provide a much more 'big cab' sound without the trade-offs and compromizes of most other 'loud small cabs'. Also, when you dig it, you won't get that loss of low end and compression like most other small, more midrange oriented cabs.
However, if pure volume and 'loudness' is the goal, there are easier and less expensive ways to get there. If 'more than a 210 volume' is the goal, with much more 'real' low end in a very small package, this continues to amaze! IMO and a bit of IME at this point.