For most people, just more bothersome, but who knows if your son is most people or not. I'd say he's less like most people, since chronic running is not normal for 2 years after tonsillectomy & adenoidectomy. Get a second opinion, consider an allergist before getting a different ENT to give you a second opinion.
Could there be something serious going on? Is chronic runny nose ever an indicator for a more serious medical condition or is it usually just more bothersome?
Rhinorrhea (runny nose) isn't always from allergies, there are other reasons for chronic rhiinitis, from environmental exposures. Get a second opinion