From reactor physics point of view, none.
But operationally they are like chalk and cheese.
Power reactors can be refuellled whereas naval reactors can't. these therefore have hugely enriched fuel and the core itself has to be replaced one the power output reduces below a certain value. Now since this is very difficult work, most AC and subs are designed for only one core replacement during their codal life and due to this, the material of construction of core is designed for much higher degree of neutron damage sustenance.