Duck -- Here are my thoughts on extended choke tubes.
Some pros and cons of extended choke tubes include:
1) extended tubes are usually easier/faster to change (usually no wrench needed),
2) most extended tubes identify the choke/constriction on the exposed portion where you can see it while some flush tubes don?t have notches to indicate choke constrictions,
3) extended tubes provide muzzle protection from possible muzzle damage (dint) that could make choke removal or instillation difficult,
4) extended tubes provide additional length which allows for the possibility of different choke geometry and design (ramp angle and length, choke angle and length, parallel section length, porting and endless marketing gimmicks) which may or may not provide improved performance,
5) extended tubes usually weigh more than flush tubes which may or may not be a good thing for your gun?s balance,
6) some shooters think the extended tubes look cool and some like the traditional uncluttered look of flush tubes, and
7) extended tubes are generally more expensive (the choke makers like that).
None of this means extended choke tubes work/perform "better" (whatever that means) than flush chokes. It really depends on the kind of performance you need/want from your chokes and loads for your type of hunting/shooting. However, if you aren't going to take the time to pattern them properly to find out how they really perform then it doesn't really matter, just use what you like.
All that said, I would ask you what you mean by pattern improvement?
Basically, choke constriction and geometry vary with manufacturers so patterns can vary from one to another even if they are marked the same, e.g., IC, Mod, et.
And, the standard Browning Invector chokes tend to have looser choke constrictions, when compared to historic choke constrictions, than some other brands. That doesn't make them better or worse, just different. The pattern board is the only way to really know how your choke/load combo is performing at any specific distance.
If you want to get some extended chokes, Carlson's chokes are a reasonable priced choke.
As far as pheasant loads, normal 12ga 2 3/4" 1 1/4 oz #5 lead loads are great all around pheasant loads.
Good luck.