Shuffle Essence! + is the definitive version of Shuffle, which was originally released in 2004. Shuffle was also the first game where Agobarrier, the now-deceased writer of the Tiny Dungeon series, made a claim to fame.
First, I should note that I originally played Shuffle in English and was not in any way satisfied with the results. My primary reasons were the low quality of the localization (though it was better than what MG had done up to that point) and certain differences with the anime involving Kaede. To be blunt, the Kaede portrayed in the anime is a solid yandere, so I was kind of disappointed that she was only mildly yandere in the game, lol.
Anyway, now to the obvious differences between the two versions of Shuffle... Well, the biggest one is the doubling of the number of heroines. Kareha, her sister Tsubomi, Mayumi, Sakura, the teacher Nadeshiko, and the new divine race girl, Daisy are the new heroines. In realistic terms, they actually consist four separate arcs... Tsubomi, Kareha, and Nadeshiko are connected loosely, with the remaining three routes standing on their own with extensive amounts of new text. This is in addition, to adding a second ending onto Shia's path and extensively re-writing it in the particulars. All in all, the length of the game is more than doubled, since the three heroine arcs are very long.
Anyway, the new routes show off something that was only touched on lightly in the anime and the original version of the game... Agobarrier's obsession with harems. Basically, the result of each of the paths is that the 'main wife' of the harem gets picked, and the girls basically make the decision to create a harem without seriously consulting Rin, since he isn't good at refusing them in the first place. If you hate harem situations, this game is pure poison, but if you like your harems, this is good stuff.
Now, to the difference between the English and Japanese versions... it does make a difference, obviously. Actually, there is a glaring difference in style between the new routes and the ones made for the original game. While the original routes were decent and tear-jerking, it seems like the popularity of Shuffle in Japan essentially gave Agobarrier license to do what he wanted with the new routes. More detail is given (including in the original heroine routes) and more loose ends are closed up. Each of the routes has a number of non-ero CGs unthinkable in a modern charage, and they are all of about as good of quality as could be produced ten years ago, lol.
Overall, the end result of this is a vastly-improved game with a much more solid cast of characters. The holdovers from the original version (abandoned stylistic issues like random cameo scenes) are sometimes jarring because of the remade aspects, but the game doesn't suffer too much from that. Daisy's route, which comes across as a 'true' route (since all the might-have-been-fatal heroine issues are resolved) seems to have been specifically designed to satisfy fans of the original who didn't like the feeling that you were 'abandoning' certain of the heroines (such as Primula or Shia) to their fates by picking another. Agobarrier loved his happy harems, lol. May he rest in peace.