Given that all previous and subsequent commodores of the era did wear a different badge to regular starship personnel, I'm inclined to favour the notion that Decker not wearing the delta would be an exception to the policy in any case.
Whether he should have been wearing the "starburst" insignia otherwise worn by commodores and the occasional admiral during the period or, whether as the startrek.com article suggests, he has an assignment that justifies a different insignia is less clear.
I prefer the idea that the various badges represented different branches in Starfleet. The Defiant crew in "Tholian Web" wore the Delta, and so did the staff of Memory Alpha. My head canon, based on the discussions I linked above, is that everyone wearing the Delta belonged to the same division or branch.