Obviously, the primary difference for Shadow is that players now have access to a variety of different weapons. There are 30 in all, and in the build I saw, they consisted of Halo 2-inspired laser swords, straightforward machineguns, and bizarre alien plasma blasters. Each weapon had a very distinct use too, with an obvious strategy for using certain weapons against specific enemies...
Additionally, the dark hedgehog could also lift certain kinds of objects to gain special items and weapons, while several of the environments were destructible and could be used for both offensive and defensive purposes (players can hide behind a boulder or throw it an enemy, for example)...
You see, each bad guy will have an allegiance to two different sides of an ongoing war that Shadow is involved in, and whether or not you help or hurt one side more than the other dictates what happens for the rest of the game. It's in this way that Shadow the Hedgehog is a bit like a "choose your own adventure"-style actioner, but your decisions just won't affect the branching storyline -- they'll affect what kind of moves Shadow can do as well...
One thing I'd like to mention is that the demo definitely kept its speed.