Here is what I perceive to be the difference.
Modern guns are the best we have ever had, thanks to modern manufacturing methods and the best steels and other materials. Even super cheap rifles like the Ruger American shoot amazingly well for the price, better than far more expensive or even custom rifles of decades past.
However, the hand fitting and finishing that went into the older guns, such as Colt's Royal Blue and S&W's hand fitting, adds character, skill, and if it can be said, soul to the gun. Every one had the skill and pride of many craftsmen go into it. Knowing that means something important. The gun becomes a work of art, in a sense; the distillation of hundreds of years of skill, experience and tradition, all aimed at providing us with a trustworthy and beautiful tool. That's why we see them differently.
Now, the new guns, of the highest technical quality, can also develop that sort of thing, but it is now we who have to add the soul. Whether it is from hunting, from using them to teach the kids to shoot, or even from using them as a dependable if battered truck gun, it is those experiences that make even the cheapest, most soulless gun into something much more meaningful.