In my little corner of the world....
I dont refer to it as a back-up gun, but just a second gun. It seems that lately a lot of folks carry service sized pistols as their CCW firearm. Thats personal choice. But I dont want my carrying every day to be a chore. So I carry a firearm designed to be hidden, one that hides well. If for some reason I feel the need to have a second gun... It's usually because I expect there may be trouble. At that point I'll strap on a second gun.. usually a service sized pistol or revolver.
For me it's also a matter of tactics. I'm a huge fan of small revolvers with concieled hammer, or hammer shroud. I can easily have a situation coverd with my hand on the gun without anyone knowing. Cops often use this technique. I used it as a cop, and use it today when doing security work. I guess I'm saying that what gun is my primary depends on the tactics. And that what is used for the second gun depends on the situation and tactics. I'm saying this as someone who own's an extensive colle....errr... accumulation of firearms and have a lot of choice.
Most folks own two or three... use what you have.