In the course of the 14 months, two double trigger Stoegers and one single trigger Stoeger have passed thru my collection. The two double triggers stayed. The single trigger went back to Stoeger permanently.
Some people can shoot the single trigger version, and some cant. I personally cant. The distance of the trigger pull is very short, and if you "squeeze" trigger rather than "jerking" it, it will reset and fire the second barrel. For me, it happened every time I did it. It sounded like one big boom. The smith's at Stoeger all tried it and they said it worked fine for all of them. It went back and forth a couple of times before they sent me a single trigger replacement for it and all is fine now.
The more $expensive "Supreme" model has nicer wood than the standard model. It also has screw-in chokes. You said you don't care about wood, but the screw in choke part means you can swap the chokes out and make both barrels pattern the same. If you have a pair of I.C. and an pair of Modified tubes you are probably all set for anything that can happen. I personally put the I.C tubes in both of them and have not felt a need to change them since. I was at the range today and I walked a couple of milk jugs from 10 yards out to the back of the 50 yard range with 25 rounds, never missing a single time.
Putting all that aside, the 3rd thing the "Supreme" model has is a fairly functional rubber butt pad. If you get one without a pad, you will be spending money to put a pad on it. The short guns do kick. The pad makes it manageable. Having survived a dozen or so incidences of both barrels going off at once with factory field loads with only minor bruising while I had the single trigger version, I am really glad I went with the Supreme model. It is nice to get one with a pad already installed.
Also, there are several variations of the Supreme. The two I have both have the S.S. receiver... a nice touch when shooting BP as it is more corrosion resistant.
Rick