Dual Canadian/American citizenship provides several advantages, which are as follows:
Immigration laws severely limit valuable public benefits, unless you are a U.S. citizen. Even green card holders face strict restrictions. Who knows what future laws will bring? With full citizenship, these exclusions disappear.
Citizens, including dual Canadian/Americans, get priority to sponsor relatives for U.S. immigration. In most cases a child born anywhere to a U.S. citizen is automatically a U.S. citizen.
Many government contracts and jobs require U.S. citizenship.
Only U.S. citizens can vote in Federal Elections. Most states also restrict the right to vote.
Freedom to live anywhere
A citizen does not have to reside in the U.S. By contrast, the immigration authorities can revoke green cards, if the holders fail to reside in the U.S. (See the FAQ question, "FAQ -Frequently Asked Questions: Canada to U.S. Immigration for Businesses and Professionals" http://www.grasmick.com/canimfaq.htm , concerning preservation of permanent residency.)
No more paperwork
If you become naturalized you do not have to worry about replacing your Green Card with newer versions. Some time ago, the INS announced the expiration of the old green card forms I-551. All people in possession of the card had to apply for replacement with a secure, machine-readable Alien Registration Receipt Card. This card expires, and you must renew it. Citizens do not have to do this.
Easy international travel
Only citizens can take out U.S. passports. Entering the U.S. is easier. Many countries waive visa requirements for U.S. passport holders. With a U.S. passport, you are eligible for U.S. citizen services from U.S. embassies and consulates when traveling throughout the world. Because of the contiguous location of our countries, this is a huge advantage to dual Canadian/U.S. citizens.
Easy domestic travel
U.S. citizens do not have to carry proof of citizenship when they travel within the U.S. On the other hand, immigration authorities demand that permanent residents always carry their green cards. The government detains permanent residents who forget to carry their cards.
Eligibility for elected positions
Many elected offices require U.S. citizenship. The ability to go into politics is more important than it may seem. Many Canadians are in demand and called upon to serve in local government. This is because of our common cultures. My retired USC clients, for example, often enjoy serving on city councils.
Finally, there are intangible advantages. Most green card holders have decided that the U.S. is the permanent home for their families. Canadians find it of psychological benefit to be on an equal footing with their American peers. Becoming a U.S. citizen is an unassailable demonstration of commitment to the country. This is important for school-age children who are very much concerned with their identity.