The joy of shooting an old gun is sometimes enhanced by something new guns can rarely match:
Provenance
Old guns often have a rich history, sometimes including having been owned or used by a respected or a notorious individual. Or, because they were used against such an individual. Other times they are associated with pivotal historic events.
There can also be personal reasons that provenance becomes important. For me, guns that belonged to my Great Grandfather, my Grandfather, and/or my Dad hold special significance. I see maintaining and hunting with their guns (especially on their birthdays) as a sign of remembrance and respect.
For others, the country of origin is the key.
Taking an old gun that is no longer functional and restoring it to its former glory is a particularly satisfying accomplishment. Then, taking the newly repaired gun out on a hunt or a shoot is the icing on the cake.
With or without provenance, let's not forget the simple pleasure that comes from walking the same trail that those who came before us walked; hunting the same game with the same gun designs that were available at the time. This alone explains the popularity of CAS (Cowboy Action Shooting, where you even get to wear the same clothes). This is also part of the attraction to black powder trails at shooting ranges.
Without question, I've definitely bought more old guns than new guns over the years.