A reactor breach would be bad for the crew certainly, but since the ships are usually always in deep water, environmental damage would be minimal. As for battle damage, a carrier would sink before the reactor could be damaged, and it is very hard to sink a carrier. Plus the navy has more precautions than civilian nuclear power plants, and the reactors are smaller.

If there is a core meltdown, the corium would just melt through the bottom of the ship.

http://www.politifact.com/truth-o-meter/statements/2008/jun/09/john-mccain/navys-record-unblemished/

https://en.m.wikipedia.org/wiki/Nuclear_marine_propulsion

That is all I can find.