The Model 10 is the basic K-Frame wheelgun and all other K-Frame revolvers stem from this "grand-daddy" of S&W's.
Mechanically, they're identical frames and internal lockworks. There are differences in the width of the hammer spur and triggers on some models. The basic difference is that the M-10 is fixed sighted while the other two are adjustable sight models.
If you were to take a Model 14 and 15 and swap barrels, you'd have a hard time telling the difference. The Model 15 is essentially the same gun as the Model 14, but with a shorter 4" barrel.*
If you have your choice of equally nice models, do yourself a favor and buy both. You'll regret not buying one of 'em later on!
* You can actually swap barrels within each frame size of S&W's pretty easily on the older pinned barrels. Special attention needs to be paid to the alignment and flash gap however.