I'll get my two cents in early to beat the rush. I fix what needs to be fixed and leave the rest alone. A "full restoration" will always be just that, with no character or history left for later owners. A good example would be a Parker pigeon gun that came to me with great barrels, a worn receiver and furniture, and the stock broken off at the wrist, with no chance of repair. Yup, a full restoration would have been the easy way out. I chose a top quality restock by Dan Rossiter with skeleton butt that matched the rest of the gun in wear. The style of stocking and forend is "Bo Whoop" including straight grip and 12" forearm with ivory inlay". No refinish of metal was done except screws. The end result was much better than anyone's full restoration. My "restoration" of classic American custom rifles would be similar, mostly addressing bad butt treatments, improper stock finish, and replacement of modern sighting.
I really like Eightbore's description above. I'd like to give his preference the term "conservative conservation", "gentle conservation", or "thoughtful conservation". It is a minimalist's view of gun renovation and it certainly has its merits. You get a gun that is improved to the point of increasing value, but without the negatives of a reduction of value from removing honest wear and character.
In eightbore's world, (and mine on some occasions), we'd target things like tig welding up buggered screws and recutting them. Perhaps a cleanout of the checkering and a few layers of oil if necessary, but not necessarily a ground up restoration of the stock. It's about retaining as much of the condition natural as is possible.
I have guns that would please the minds of eightbore and his kin quite a bit. On the other hand, I do like a ground up restoration to as-new if the gun was a good candidate for that activity as well. In lieu of buying a soulless new gun, there is beauty and history in a completely rebuilt gun by a known maker. There are Brit gunmakers that rebuild their 100 year old guns to as-new, bespoke to the new owner. There is beauty in that as well.
I find that the condition of the engraving, case hardened finish and overall metal condition is what drives my decision to "thoughtfully conserve" the gun versus "holistically restore" a gun to as-new.
I think those that adhere to eightbore's mantra get one additional point of preference: when a gun is thoughtfully conserved very little has been undermined with the gun. On the other hand, once a gun is full brought back to as-new there is no going back and the value/interest of the gun has been permanently altered.
This debate is no different than the collector car crowd. Some want as-new "living legends", others want to compete in the "survivors" class with original paint, original seats, as original as possible in every way. (as you can imagine, there are fewer and fewer of the latter)
