Wasn't too sure what the Model 620 was until I looked it up. From what I could determine, S & W is dropping all K-Frame revolvers, and the 620 is an L-Frame successor.
So, in essence, the only difference is the full lug barrel. I own two Model 586 guns, both early L-Frame blued guns, one a 4" and the other a 6" gun. My own personal preference has been toward muzzle heavy guns, and the 586/686 fits my wants perfectly. The weight out toward the muzzle seems to get me on target a little faster, and dampens recoil more, though with a .357 Magnum recoil is not that much of a problem.
If I were buying, I'd go with the full lug barrel.
Here are some of my Model 29s, two with full lug barrels I had S&W make up for me many years ago.