To me the main difference between the two are as follows:
SASS is a shooting organization with (a very) minor emphasis on authenticity.
NCOWS is a Re-enactment group with emphasis on authenticity and minor emphasis on shooting.
(Note: this is not to say shooting is not important in NCOWS, but its not the main reason to be a member.)
For me... I had been in Buckskinning for years and then decided that I wanted to get into the Cowboy period. I thought SASS would be like Buckskinning only re-creating a later time period (mid to late 1800's). I was wrong. Yes there are some in SASS who try to be authentic but many only dress just enough so they can shoot. And the main emphasis is on being competitive. I did join SASS and am still a member, but I became a Life member of NCOWS even though the opportunity to shoot in NCOWS is slim to none. My personna is an ex-Confederate Guerilla/gambler and general no good outlaw. I shoot .44 Remington '58's, a Henry .44-40, and a 12 Ga Mule Ear (I am kicking around getting a double barrel 12 Ga Muzzle loading shotgun). I have purchased everything from Civil War Suttlers, I have a haversack, cap pouch, Pistol Cartridge Box, Cavalry Carbine Box, and Rifle Cartridge Box so i can switch around as needed to carry all my equipment. Civil War Era Wallet, eyeglasses, combs, penciil, spurs, Cavalry Boots, you name it.
You can belong to both and act as an example of NCOWS authenticity at SASS matches.