Nuclear powered ships
Nuclear power to power a ship is linked to the sideeffects of this form of energy and propulsion, namely nuclear weapons and capabilities. Therefore a surfaceship, no matter which one, with a nuclear propulsion can be as easily combatted as any other type of surfaceship, especialy by the relatively cheap submarine of the early Cold War period, of which type the USSR possessed quite a number.
Nuclear power is only proffitable in strategically important naval vessels, which are not battleships, but the large CVB's, capable of delivering a nuclear strike themselves, when asked to do so, and the SSBN's, with their equally important SSN's as both escorts and ASW vessels.
The only real drawback of nuclear propulsion is its pricetag. Only the largest surfaceships, which are large aircraft carriers normally, can be so equipped, as the carrier then has more space for storage of Aviation fuel and weapons, in stead of its own fuel.
Nuclear powered surfaceships are to last for many decades, or they will be considered too expensive. This means only the relatively simple large aircraft carrier, which has only a small armament itself and therefore sensor network, can be nuclear powered, as this type of vessel is to last for some 50+ years normally, because its more specialized escorts are to defend it against newer threaths. These are conventionally powered, to reduce their production costs, as they are not expected to last as long as the carriers.