For carrying, the Model 66 is a little smaller and lighter in weight. The K- frame S&W 357 Magnum was designed for law enforcement officers who would practice with 38 Special, qualify with a few cylinder fulls of magnum ammo, and carry magnum loads. At that time, the most common bullet weight for the 357 Magnum was 158 grains.
As more officers and agencies switched for practicing with 38 Special to practicing, qualifying, and carrying 357 Magnum, and the switch to 125 grain bullets, forcing cone erosion and cracking at the bottom of the forcing cone became a problem. To fix this issue, S&W developed the L-frame 586/686.
If you plan to shoot mostly 38 Special ammo and keep the 125 grain magnum ammo use to a bare minimum, the K-frame is fine. If you plan on a steady diet of 357 Magnum ammo, then the L-frame is a better choice unless you buy one of the new, Model 19/66 Classic revolvers. These would be the Models 19-9 (carbon steel) or 66-8 (stainless steel). The 19-9 and 66-8 have completely different barrel design that eliminates the flat spot at the bottom of the forcing cone.