Size, scope is probably the biggest:
The demo takes place in a tiny part of the available world: Macedonia. The full game...well, you have the entirety of Greece, north into the Balkans, and east all the way to Turkey.
Freedom is the second biggest:
In the demo, you have a fixed set of missions to complete. In the full game, you can pick and choose where to go, what to do.
There are lots of other things you get to do in the full game, such as learn Trireme tech that lets you explore the sea, etc. LDA can probably give you a better overview than me :)