What's the difference between the two? What is better for what?

Is this a trick question? One has two barrels, one on top of the other - the other has two barrels next to each other.

Both are generally considered most at home hunting upland game, but it's generally personal preference. I like the more robust forearm and "cleaner" field of view the O/U offers. Neither are good in a goose pit, nor are they particularly well-suited to hunting big game with slugs or buck (although I'm certain it could be done).

I love my O/U and hate side by sides. Doubles are supposed to be fast pointing as they are shorter due to no receiver. Nothing beats a double pheasant hunting. Now if we only had pheasants in Wisconsin like we used to....

I like SxS's in sub-gauges, and 12 gauge for O/U's.

I am an O/U guy who has a couple of Brownings that I use for pheasant, grouse, and woodcock. This year the wife bought me a SxS, an old Parker, for my birthday. Apart from it being a classic, I was surprised by how well I did with it. Now if I can only figure out the twin triggers. Apart from being much more familiar with an O/U, I can't see the advantage of one over the other for upland hunting. It is a matter of personal preference.

One of the distinct advantages to an O/U over an SxS, however slight, is that since the barrels are vertically alligned, they track the same. Side by Side barrels are actually regulated to cross in front of the bead at a given range (25-50yrds for most models), but ultimately, the shooter is NOT looking down the centerline of the bore. For O/U's, the barrels are regulated vertically again at a specific range, however, they won't track left to right like a SxS will, since the shooter is actually looking down the centerline of the bore.

You only usually notice this "crossing" when you're shooting slugs. I installed .45-70 sleeves in a SxS that was regulated at 25yrds. At 200yrds, the left barrel was shooting over an inch to the right, and the right barrel was hitting about an inch to the left of the POA. Each barrel would shoot approx 1.5-2" groups, but the groups were distinctly off center.

Of course, 2" for a shot pattern isn't really critical. And of course, with the O/U, I'd expect vertical stringing too.

Beyond that, O/U's are generally considered to be better balanced, and more stable for fast action clay shooting.

Personally, I like both. I'm more of a fan of the style of a SxS and I knock down a lot of birds with them each year, but I break more clays, for some unknown reason, with my O/U's (honestly may simply be practice).

I personally like an OU more than a SS. You don't have to try to alter your line of sight with an over under.

I will take my O/U's everyday. I have them in Browning Citoris, Beretta's and my Kreighoff.
I had a SxS and was lucky to have been able to hit the dirt with it, even on a good day.
I use them for trap, skeet, dove, duck, pheasant and goose.

Before there were O/Us there were SxS...I grew up using a SxS for everything...From deer with buckshot and slugs to rabbits, squirrels, doves, ducks, geese, turkeys, crows and quail, she has done everything...She has a modified and full choke...When quail and dove hunting, I use cheaper low brass shells which helps the modified choke open up quicker...

I prefer double triggers over single, once you get use to them you usually pull the more open barrel first as the game is usually closer...The tighter barrel is used second if you miss...When squirrel hunting, I usually use the full if the squirrel sticks his head around the tree and the modified when they are jumping from limb to limb...

I guess a O/U is OK, but the SxS is the traditional upland game shotgun...No real advantage of one over another as it's what you get use to...

The real difference is in waterfowl hunting and the need to use a plug.

With the side by side you don't need a plug for either the right or left barrel but when using an over under you don't need a plug for either the upper or lower barrel.

It's really that simple!