When Mossberg and Federal got together to produce the first 3.5" chambered 12 gauge shotgun and the shells to fit it, they were trying to help those of us who shot waterfowl, who had been forced to shoot non-toxic shot (steel then) get a killing load. The longer length allowed more of the larger steel shot to go in the shell.
Turkey hunters demanded the 3.5" gun (larger payload) and gunmakers and shotshell makers soon obliged us by trotting out a number of different camo guns and shotshells.
Over the years I've patterned a lot of shotshells and here's what I've found. All things being equal, a 2.75" shell will pattern better than a 3" shell and a 3" shell will pattern better than a 3.5" shell. There are certainly exceptions and I'm sure somenone has a gun that patterns a longer shell better than a shorter one but that's been my experience after firing a few thousand at "big paper". When I say pattern, I also mean consistently, at least 10+ shells, not just 1 particular pattern that comes from a "hot shell".
Shotshell manufacturers and choke makers have learned so much in the last 10 years or so about performance of their products and for the most part, the shells and chokes are so much better, I don't see much if any need for the 3.5" gun today for us as turkey hunters.
In most cases in my experience, compared to the 3.5" shells, the 3" shells pattern better, they cost less and they kick a lot less, I only recommend 3" shells for turkey hunters, even if they have a 3.5" gun.
If however, you are a waterfowl hunter and shoot steel shot, the increased length of the 3.5" shell will allow you to have a larger payload of big shot needed to kill those birds.
This brief excerpt may help a bit.