No difference I have ever heard about except the barrel and front sight, the shape of the top strap, and possibly the front of the frame. Some versions of both models may or may not have had trigger stops. Probably some other minor things, depending on the various engineering changes and individual guns one might bump into.
I am one of those guys who tends to shoot the Model 15 better than the 14, especially the lighter barrel versions of the Model 14. The wider rib of later 14s shifts some of the weight forward and favorably changes the balance and recoil impulse for me. To further complicate things, there are the 14s with the full-lug barrel. I always thought it would be nice to have one of those in 4-inch, but never saw one to buy. I do have a 6-inch, and it is nice gun in some ways, but does get heavy when you handle it over a long session at the range.
Overall, I prefer the heavy barrel version of the Model 15 (15-6?) for my casual .38 Special shooting, but that’s strictly an operator thing, not that one model is inherently better than another. I’m sure any version of either model can outshoot me any day, all day.