Since recently I answered to this question at two different forums - so, what are the differences between Samurai Shodown 5 and Samurai Shodown 5 Special?
Character cast
Although its almost same, SS5sp has more playable characters by adding Amakusa, Mizuki, Zankuro and Gaoh (the 4 bosses) to playable roster. Unplayable sub-bosses Sankuro and Yumeji were removed together with comical extra Poppy.
Stages
Games use different sets of stages, the only recycled ones are 4 stages of new characters from SS5 (Yoshitora, Mina, Yunfei, Kusaregedo), although their appearance was heavily tweaked for SS5sp to fit its darker aesthetics. SS5 stages were generally very bright, colorful and pastel-like, while SS5sp ones are more empty, dark and menacing (unfortunately they are also more simplified and bland). Since SS5sp has 4 playable boss characters, their 4 stages also make appearance as regular stages in game.
Music
SS5sp has new music themes including remix of "Bushido" intro theme and brand new select screen theme. Soundtrack for the game was never released, although you can listen to the tracks using Kawaks. There are many silent, ambient themes fitting for game's overall style. Tracks recycled from SS5 are used in Yoshitora's, Mina's, Yunfei's, Kusaregedo's and Gaoh's stages.
Balance
SS5 isnt very bright in this aspect, having god tier Yoshitora and several other balance issues (like Yunfei's wall jump quadruple flight runaway game). SS5sp had undergone heavily testing and several location tests, and now is regarded as most balanced game in series (despite having the large 28 characters cast). In SS5sp, various gameplay aspects were tweaked, few moves were disabled, you are unable to execute part of combos possible in SS5 but characters may have new ones instead etc. For example Suija's waterballs became slower and less spammable, while he got more opportunities to cancel into his aerial moves from ground compared to SS5. SS5sp also introduced new gameplay element - Death Ougi, which counterweighted State of Nothingness & Issen system previously abused in SS5.
On high level many characters play differently in both games (new combos are enabled and some of the old ones are disabled, few normals differ, etc), so there is a point those two should be treated differently, but because most people dont play on high level, and SS5sp has nearly all cast members of SS5 already, most people just dont bother to play 5.
Interestingly, some of elements introduced in SS5sp can be found in original SS5 code, which led to speculations that SS5 was essentially an unfinished game and SS5sp was what developers originally aimed for SS5 to be.
Violence
Was generally absent from SS5, together with finisher moves - although enabling full violence in SS5 resulted in working suicide moves. SS5sp on the other side, is the most bloody game in series, having wide array of generic "split in half in different way or smash into wall" finishers activated by normal attacks at the end of battle - plus character-unique instant kill "Death Ougi" moves that ended the match in very gory fatalities.
Secret Moves
SS5sp introduced few easter eggs from developers, like a superspeed mode for Enja, unblockable Plasma Factor slash for Galford, and 14-hitter combo for Charlotte. Those should be activated with special command first, before they can be used as regular moves.