Each of an aircraft carrier's rectors(they all have 2, except for the Enterprise which has several submarine reactors) are indeed quite large. The reactor itself is 3 stories tall, then you have the primary system whose pumps are as big as submarine reactors. Then, you have the steam system(which is quite large-it's the rest of the heat cycle).
On a carrier, they take up the space directly under the mess decks. Although, if we were just going to use them for just electrical power(or, in the case of the spacecraft, heating a gas), they could be considerably smaller.
Also, submarines aren't terribly large. A submarine reactor is only like 12 feet across(but then you have the rest of the systems).