Advantages- Nidoqueen has more bulk than Nidoking so, that makes Nidoqueen a good Pokemon to set up Stealth Rock and Toxic Spikes.
Disadvantages- Nidoqueen has less offensive power than Nidoking. Making Nidoqueen offensive isn't that good of an idea.
Advantages- Nidoking has good offensive stats. It could do some damage to your opponent.
Disadvantages- Nidoking has poor defensive stats. A super effective hit on Nidoking could make it faint.
Summary- If it were up to me i would choose Nidoqueen because it has good defenses and it can learn Toxic Spikes and Stealth Rock. That is just my opinion if you need an Offensive Pokemon in your team go with Nidoking, if you need a Defensive Pokemon in your team go with Nidoqueen.