I haven't got a combo, but I felt compelled to answer, anyway...

I'd opt for an o/u shotgun/rifle combination.
The shot barrel in 12/70, half choke (I don't see any use for magnums, and additionally the existing shotguns in the house are 70mm so there'd be no risk of accidentally feeding magnums into a non-magnum gun!).
The rifle barrel I'd like to see in 7mm, probably 7x57R, but even a 6,5mm would do, and nothing larger than 8mm.
The use would be to have a rifle when bird hunting: often there are doves on a field too far for the shotgun, and then the rifle barrel would step in. This problem I encounter every year when duck hunting, and me and my hunting buddy always also go looking for dove. You know: "Shall I take the shotgun or the rifle?" Not wanting to carry them both.
The other good uses would be on roe deer and whitetail deer. For the whitetail I'd load the shot barrel with a slug, but with roe shot could be used. Also this'd be a potent combination for wild boar! Unfortunately, in Finland no use of shogun even with slug is allowed on elk, so then the gun'd only be single-shot.

My father'd buy a drilling in 20 gauge/suitable rifle barrel, 6,5mm to 8mm.
What use? Well, it'd be nice to have... If you have such a gun, you never need to think what to take, you just grab that one drilling and a pre-loaded ammo belt!
The 20 gauge would make it fairly light and not too noisy, which would make it useful in areas where there are lots of summer houses and like.

Whyn't I have one, then?
Well, when bird hunting a double-barreled shotgun is more useful as the 2nd shot is often needed.
In the scenario of the dove the situation only comes up once a year for me so I can live with the irritation but it does not really justify the acquisition of a combo.
For all else of my hunting a rifle is frankly a better choice as the shot barrel really would not have any value-added for the hunt.
My brother, again, mostly hunts small game like birds, furred animals, rabbits and like, and for him I could certainly see the combo being very handy, indeed, with a small rifle barrel like a .223.