There is a significant difference in POI between the two barrels, and/or
Some folks believe shooting the lower barrel reduces perceived recoil and barrel jump (and therefore stock movement into yoru face) due to the fact that the bottom barrel is more lined up with your shoulder.
I shoot with many folks who shoot the top barrel for singles and handicap, and can't tell the difference.
Both my barrels shoot pretty much the same POI. I just shoot the bottom barrel because I like to, and it has ever so slightly lighter trigger pull weight.
It is the vertical distance between the barrel fired and the heel of the stock that accounts for the difference in barrel rise in the two barrels. The lower barrel is more in-line with the bore and results in reduced barrel rise.
Other factors can also affect perceived or actual barrel rise during recoil. The most important is the drop at the heel dimension - how crooked the stock is. If you look at stocks made several hundred years ago for shooters wearing high, stiff, collars, you can see drops at the heel approaching four inches. The stocks had to be crooked since shooters could not lean their necks forward to place their cheeks on the combs. It was with improvements in gun design and heavier loads that prompted drops at the heel to be reduced and shooting apparel to be redesigned.
It could make a difference if the gun has fixed chokes. One of my O/U's has an IM in the lower barrel that patterns well for singles and mid caps. The POI is also a bit higher than the top barrel. The top barrel has a very tight choke with a very dense pattern center, which I don't find desirable for singles, along with the lower POI. If you gun has fixed chokes, you would need to determine which barrel is best by some patterning and experimentation.
In a nutshell, if you have different chokes in the barrels, then one may be preferred for singles while the other for handicap. Then, the mantra is that there is less felt recoil in the lower barrel than the top but I've never been to feel any remarkable difference....breakemall....Bob Dodd
Here is another theory I have heard proposed...since the bottom barrel is closer to the hinge and more in a straight line with the gun axis, there is less pressure put on the locking lugs than if the top barrel is shot extensively...take it for what it's worth.
Shooting the lower barrel first is the traditional firring order. This tradition may be based on a slight difference in barrel rise but this difference may not be consistent with every shooter and every gun.
Neil stated above that he feels more recoil from the bottom barrel than the top. This might be due to the characteristics of his gun, his characteristics or a combination of both.
I shoot the bottom barrel first in doubles because when I put on my un-single barrel, I must shoot only the bottom barrel. If I changed the firing order for doubles I would not remember to change it back for singles and would get many more failures to fire.
My personnel habit and mental need is that I shoot a tight pattern, mentally when I have tried to shoot the more open lower barrel I loose more birds by being careless, when I shoot the tighter over barrel I tend to concentrate more!
I can not perceive any differrence between top and bottom in recoil!