There is no way I could honestly say IV is better than III. I have some fond memories of SSIII, granted not as many as SSII or SSI.
Seriously, how often did SNK completely redo the graphics and game engine for their sequels? How many times have you heard someone say something like, "I wish they would redo all the sprites in the next KOF game even if they had to cut down the roster." This is essentially what SNK did with SSIII in 1996. They also did this with KOF96, but thats annother story.
At the time of its release, these graphics were simply amazing. The only game I felt even came close was Xmen Streetfigher, which had big sprites, and lots of special effects, but didn't have the cool Samurai atmosphere that made 3 one of my favorite Neo Geo Games of all time.
SSIV is cool, I like the character roster, but its mostly made out of Pallet swaps from SSIII. SSIII had a much better atmosphere and was nicer to look at. Except of the selection screen.
I feel Samurai Shodown went a little like this
2>3>1>4
I won't comment on V, Vspecial, 64, or 64II cause I haven't really played them. I doubt any of them are better than SSIII though.