That is what they call a "lateral upgrade",
You would get a slight improvement--maybe, if you hold your mouth right etc.
I am assuming you have ONE subwoofer? If so, if you expect/demand an improvement--I'd pick up a second RBH to match your first one.
This way you'll gain at least 3dB of output (or more) and you'll get a more even bass response around your room. The natural peaks/nulls that happen in smaller rooms will be "filled in" by the other sub if you do proper setup. The reason for this is a single sub will have peaks/nulls and so will the second sub--but they will be at different frequencies so the nulls will be "filled in" by the other sub. They do if you don't stack them on top of each other, read up on proper setup of dual subs to assist your setup. You can't EQ out a null but you can a peak so a combination of EQ'ing the peaks and "filling in" the nulls with the second sub is how it works.
Then of course, if you want more--you will get introduced to the "rabbit hole". Three subs will give even better response (Look up Earl Geddes and 3 sub setup) or 4 subs might fit your room better (corner load all of them to gain more "free" output.
Chasing better with one 12 inch sub might get you a little bit--but 2 of the same subs will give you better bass sound quality and a bit more SPL. If it was me, I'd go with a second RBH for a known improvment. Now if you can only have one sub for whatever reason--and it must be a certain size then you have to deal with that issue. At that point, if I could have only one (one sub to rule them all!) I'd go with the highest performance with a sub in the largest size I could handle. We all have to deal with reality at some point--reality sucks.
Good luck in your quest, let us know if you can do 2 subs (or more) the maximum size you can deal with and how much SPL you wish to have, what frequency range that you desire and all that jazz. Hope my babble helped more than it hurt--enjoy!