Gauge means nothing to the target. Shot is not a single projectile.
The bird has no idea what gauge shotgun you used. The few pellets that hit the bird are what matter. A #4 pellet going 1000 fps will do the same thing to the target, no matter what gun it came from.
Bigger pellets hold more energy at range. That's why pheasant hunters use #6 to #4 as Larry wrote.
The reason for a larger gauge is not because it hits harder, but because you can load it with more pellets and still get a decent pattern. Also, a larger bore will pattern better with larger pellets, since they can arrange themselves more evenly in the wad.
Consider a wheelbarrow full of large rocks vs. one with gravel. The large rocks in the wheelbarrow have a lot of spaces between them, and they don't flow if you dump the wheelbarrow. Gravel flows almost like liquid. A railroad hopper car full of large rocks is a lot like a wheelbarrow full of gravel, and with enough space to work with, the big rocks flow like gravel when you dump them.
A standard 28 Gauge load of #4 is 101 pellets, and I'm not sure how well that big shot patterns in a small bore. It most likely doesn't pattern as well as you'd like, and increasing the payload will just make that worse.
A standard 12 Gauge load of #4 pellets is 151 pellets, and you can load a good deal more in a 12 Gauge and still get a good pattern.
So, 28 Gauge is not too light. A pellet is a pellet is a pellet, and 1200 fps is 1200 fps. But your pattern will either have insufficient density at longer ranges, or you'll have to choke it down too much to use it at closer ranges and you'll wreck the pattern.
There's no reason a 28 wouldn't work at close range, but I was out pheasant hunting Sunday and those things flew straight away and fast. There weren't many close shots.
I think 16 Gauge is just MADE for pheasant.