Backround of these two films as I have heard it:
Barboni, upon hearing that Troublemakers was in pre-production wanted to direct it and contacted Terence Hill but he wanted to direct it himself. Barboni was very bitter for this as he thought that he was the man behind Trinity films and the one who made Hill & Spencer duo so famous. Trinity & Bambino: The Legend Lives On (aka Sons of Trinity... what a nonsense title! They are not both sons of Trinity in the film!) is Barboni's answer to Troublemakers, the true sequel to two Hill & Spencer films according to him. Knowing that Hill & Barboni were not in best of terms I suspect that Barboni has (had) copyrights for Trinity series and that he prevented Hill from using those names on Troublemakers. It seems very logical thing for him to to do in such case.
Anyway, Trinity & Bambino is better of the two IMHO. Lead actors are not great but they do their job and the films has real "Trinity feel" to it, which is not the case with Troublemakers. I don't think that Barboni could have saved Toublemakers because overtly sentimental scenes ruin much of it regardless of director. But to see Trinity & Bambino with Hill & Spencer on starring roles... it would have been the best Trinity film for sure!