Dominions is more like Risk. You build armies and conquer territory and try to push the other guys off the map. Any given map is generally considered to be the whole world, given horizontal-but-not-vertical wraparound. Combat itself is almost entirely hands-off; it is controlled by how you prepare (including simple [or complex] scripts for magic using units, equipment, selected units), but when combat actually begins between two armies you have no control. There is very little province management: there a couple things you can build in a province but unless the province is particularly valuable in some way, you probably won't build anything (instead using those resource to recruit more for your army). Army movement is largely one-province-per-turn with some restrictions. The magic system itself is incredibly broad and a lot of spells require the spellcaster to invest into multiple branches of magic (paths?) in order to use the spell.
AoW is narrower in scope. Any given map is considered just a "region". There's more empire management involved in that you have to collect resources separate from merely owning territory (as in Dom) and you can build and develop cities to improve their economic output and to recruit more advanced units, and you have direct control over units during army combat. While both the region and combat maps are tile based, movement varies by unit and is generally several tiles per turn. Magic is, I would argue, quite limited, since there are no cross-sphere magics at all: you don't have access to new or different spells just because you selected fire and death as opposed to fire and water, for example.