The K-38 Masterpiece is the Model 14, and S&W continued to call the Model 14 the .38 Masterpiece for years; the only difference is the model number stamped on the frame. The .38 Combat Masterpiece is the 4" barrel version with a ramp front sight; neither of those guns is a Combat Masterpiece, and the OP doesn't have that choice.
I see no practical difference in the guns; both have the target hammer but not the target trigger. To me it would be a matter of whether one individual gun is in better shape than another individual gun.
Jim
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