For skeet you will find that most shooters prefer a gun with a 50/50 Point of Impact or POI
That means that half of the pattern will be above the sight plane and half will be below. This is ideal for crossing targets, such as those found in skeet.
A skeet gun should balance between the hands, preferably at the hinge in the O/U
A skeet gun should not be too light or to heavy,
if its too light it is whippy and has a lot of recoil and muzzle rise which makes the second shot on doubles more difficult.
Too heavy and it can be hard to get moving and if your are to vigourous and beat the bird hard to slow down before its too late.
Ideally a skeet guns is around 7-3/4 lbs to 9 lbs with a subgauge tubeset.
A trap gun ideally has a heads up shooting style, ie montecarlo stock etc.
A high adjustable rib, and most believe now a higher POI
People nowadays like 70/30 or even 90/10 this way you can keep the target insight and follow it and break it.
I find when shooting trap the barrel in relation to the target in more precise and critical, in skeet the targets are always much closer and leads are larger.
With trap you use tighter chokes and have a smaller pattern and are shooting the target a further distance, a gun with longer barrels, high ribs and stocks all make this easier.
A trap gun should be fairly heavy, to help with felt recoil, trap is a faster paced game and recoil is the enemy.
Finally sporting clays.
This is not my area of expertise but here it goes.
Sporting clays guns are typically very light, usually use imp cyl and mod or imp. mod and mod chokes.
The often have a POI that is tad bit higher than 50/50 perhaps 55/45 or 60/40
They balance between the hands very well, have instant pointability and come up very easily, the stocks have larger amounts of drop at heel to help with the quick mounting that most shooters use.
Automatics are very popular in sporting clays but so are O/U
Competitive Trap is mostly dominated nowadays by single barrel double barrel combination O/U
Skeet is mostly dominated by O/U as well but there are always going to be shooters out there with semi and pumps.
Hope this helps and I didn't make too many mistakes