I have a 686 and a couple of the 64's carbon-steel sibling, the model 10. For home defense either is a fine gun, and I keep mine loaded with the FBI loads (158gr+P LSWCHPs), which have been well-proven in use by law enforcement agencies.
The 686 is a bit larger and heavier than the 64, and it has the full length barrel underlug which adds weight out front and helps reduce muzzle flip when firing magnums (which always draws attention at the range due to the loud report). With .38 specials the 686 has minimal recoil and is very easy to shoot rapidly. The adjustable sights are nice because you can set them for whatever load and range you are using, but this is hardly a factor at across-the-room or down-the-hallway distances. If you are thinking about adding tritium night sights, then you can do so with the 686 as long as it has the pinned front sight. The 686+ gives you a seventh round if that is a consideration for you.
The 10/64 is a bit lighter and more compact than the 686, owing to a smaller cylinder (the 686 cylinder and forcing cone are beefed up for extensive use of magnums). The 10/64 and 686 both have exactly the same grip frame and trigger reach, but in my opinion the 10/64 has a nicer balance and is a little quicker handling. I find it quite easy to manage with the FBI loads. I regularly carry one of my model 10s.
Both guns are exceptionally accurate and fun to shoot.
Handle both if possible to see which one feels better to you. If you are married and your wife may have to use the gun also, let her handle them as well and get her input.
You might also consider the Model 66, which is sort of the best of both worlds. It is the size of the 10/64, stainless steel, has the adjustable sights of the 686, and can fire .357 magnums, though you will get various opinions about how often you should shoot it with magnums and what bullet weights to use.
Sorry about writing a novel, but these are great handguns and easy to go on and on about. Hopefully my opinions will be of some value to you.