I had a B-SE back in the day. On mine, the right barrel was modified choke and left was full. The right barrel fired on the first trigger pull, left on the 2nd. No way to change it.
At the same time my most frequent shooting buddy had a Model B. I liked the Model B and it seemed I couldn't miss with that gun. I subsequently bought a Model B and like it much, much better than the B-SE -- still have the Model B today and it's one of my all-time favorite shotguns to shoot of the 15 or so I've owned. The Model B is much more ruggedly built (the single trigger and ejectors in the B-SE just felt flimsy, and in fact I had a bit of trouble with mine because they just weren't robust enough), and has double triggers which I prefer in a SxS, and just has extractors instead of ejectors.
This latter is good with me because a.) I keep my hulls for reloading, and b.) ejectors are likely to give trouble eventually in a lot of guns (especially those like the Savage Fox that cost a few hundreds of dollars instead of a few thousands).
My advice, find a Model B instead. You should be able to buy a pristine one on GB for about $450.
Edited to correct the left/right chokes and order of firing in the B-SE.