Quite a bit actually from the ground up.
SR is designed to challenge the SP game. And they do accomplish their goal. It is a very challenging SP game at normal settings and at hard stteings, you had better be one of the better players. the AI is given quite a few advantages compared to the player, and the AI files themselves are honed to be quite fierce. BEWARE!
CORE is designed at giving a deeper experience. there are a great many more events, particularly for the non-major countries. not only historical events, but even quite a few ahistorical turnings are pursued quite far. while more difficult than vanilla HOI, the difficulty comes more from complexity than in actually changing the odds against the player. CORE is [will be] thus well suited to MP as well.