I have an IGA Stoeger and a Winchester '97 pump. As to which is faster-it depends on the shooter. A double is a heck of a lot more reliable. You should start with a double and practice loading it,as this is where a lot of time is spent on a stage. The shooter who's efficient with the shotgun will beat the other guy who's not.
A lot of folks shoot Stoegers. I see a lot of the newer shooters with EAA Bounty Hunters,but I've never shot one. Any new double you get will benefit from an action job.