Pros and Cons to Getting US Citizenship
Your chance to participate in steering America in the right direction.
Naturalisation is the only way to guarantee you have the right to remain in the US. PRs are at risk of losing their status if they spend long periods of time outside the US or commit certain, sometimes not very serious, crimes.
Your dealings with the US immigration authorities finally come to an end and you no longer have obligations, for example, to inform them of your change of address. Also, you will release your spouse or joint sponsors from financial responsibility of sponsorship under the I-864.
Some US permanent residents are restricted from access to public benefits, especially from receiving them whilst abroad. This is a continuing and deepening trend. This can include access to Social Security benefits.
You are able to serve on juries and participate in the criminal justice system.
Unlike USCs, green card holders cannot sponsor parents or siblings, and USC receive priority for spouses and children.
Most types of elected positions (as well as appointed positions) require the officeholder to be a USC.
USCs and PRs are not always treated the same for tax purposes. This is particularly true for federal estate taxes, where the exemption from estate tax for spouses does not apply if the surviving spouse is not a USC. In that case, for 2012, any estate over $5m is taxable. From 2013 and onwards, unless Congress legislates, the exemption falls to $1m.
Some federal grants are only available to US citizen applicants.
Most federal government jobs and many state/local government jobs, require the applicant to be a USC. Most (but not all) state and local police forces, for example, require USC to become a police officer.
Some government-related jobs in corporations require a USC, especially in the energy and defense sectors.
Security Clearance, for the above type of jobs, with citizenship, you can have a higher level, but don't forget that having ties to the UK via friends, family, property etc might still limit the level of clearance you may gain. In addition, some clearance levels (e.g. NOFORN) are generally not available to dual citizens. Even USCs who renounce foreign citizenship may have difficulties with high level security clearances due to other foreign ties.
As a USC you are entitled to a US passport (which may have better visa-free travel) and to consular protection from American missions overseas. However, US consular protection is not available in any other country of which you are a citizen.
USCs have simplified access to work permits in Canada and Mexico due to NAFTA treaty provisions.
As a naturalized USC you will normally meet the physical presence requirements to be able to pass on US citizenship to children born outside the United States. In cases where these are not met, you may sponsor them to the United States as immigrants and have them benefit from automatic citizenship on admission to the United States as immigrants (if under 18).
Most states allow Green Card holders to possess firearms, but some (eg Washington State) require any non-citizen to have a permit. As a USC you will be exempt from these requirements. Also, many states will only issue "concealed carry" permits to USC applicants. Furthermore, the rights of Green Card holders to own and use firearms could be removed by federal legislation in future. As a USC your rights to own a firearm are protected by the Second Amendment.
In a few states, one of which is Alabama, you may need to be a USC in order to get a professional license, such as become a Certified Public Accountant (CPA) in that state.
Your photograph and fingerprints will not be required under the US-VISIT program on entry to the US. If the port of entry is operating an entry channel for US passport holders only, you may use that channel.
Depending on state law, there may be a requirement that if you want to adopt a child, one or both adoptive parents must be a USC.
Being a USC won't keep you out of jail if you are convicted of a crime, however you will likely be deemed less of a "flight risk" in terms of eligibility for bail and/or time in a minimum or low security jail. Depending on treaties, being a USC could mean you cannot be extradited to certain foreign jurisdictions.
If you are not a USC this might go against you in any child custody dispute before the courts (depends on state).
You can no longer escape this by ticking the non-citizen box
There may be dual citizenship issues for some. However this is a not a problem for UK citizens since the UK government has no particular issues with British citizens holding dual citizenship. For the US perspective, which requires a few rules to be followed, see http://www.richw.org/dualcit/
You are now liable for US tax on your worldwide income if you leave the US. Unlike most other countries, US citizens pay tax on their worldwide income, regardless of where they are living. So if you move to the Cayman Islands and live there 20 years, you are still required to pay US taxes. This is a very important point to note. Tax Treaties with certain countries mean you will not be doubled taxed if you paid taxes on monies earned in that country to that tax authority.
Also note that if you wish to maintain your PR status while living abroad for a year or two and have the appropriate re-entry permit, you must continue to pay US federal taxes (plus in some cases, Social Security + Medicare tax) as proof of unabandonment of residency. In addition, since you normally have to keep a US "home" you may have to continue paying state income tax, while a USC could usually claim to have abandoned a state domicile.
So if you will be spending the rest of your life overseas and never coming back to the USA, becoming a USC will carry a disadvantage of filing and paying for USA tax. However, if you are only going outside the USA temporarily and want to keep your green card, then (among other things) you have to keep filing and paying USA tax anyway and you might even have to pay additional state taxes.
US citizens are required to annually report any foreign bank account that has over $10,000 US in it at any time during the year. These FBAR reports are filed separately from your taxes, and the penalties for failure to file are steep. In addition, another new law called FATCA requires filing for higher amounts (it's a sliding scale). It also requires oversea banks to report on US customers. In some countries this has led to banks refusing to hold accounts of US citizens. Finally, should a US citizen own a certain percentage of a foreign company (like > 10%) than there is a rather complicated form they will be required to fill out called IRS Form 5471. Information Return of U.S. Persons With Respect to Certain Foreign Corporations.
All males on their 18th birthday must register for Selective Service, aka the Draft. This is the list of names that can be called into military service in times of national need. It was designed to give the US the troops that would be needed to repel a Soviet attack in Western Europe, and despite the fact that isn't very likely, it's still on the books as a requirement for all males aged 18-26 years.
Are now a no-no! (although this is also the case for green card holders and even temporary residents of the U.S.).
The Embassy of your home country will no longer be able to intervene on your behalf with the U.S. authorities (since they can't get you out of jail anyway, this is a limited benefit).
As a USC you will generally be ineligible for a diplomatic position with your home country's embassy or consular service in the USA, although you may still hold positions designated as "locally engaged" or "honorary".
 OTHER CONSEQUENCES
A US citizen domiciled abroad can not sue in diversity (or be sued) in federal court, whereas a non-US citizen can.
A naturalization application results in a complete review of your immigration history before final approval. If there's anything in that record which might by problematic, it would be prudent to consult with a qualified professional before awakening the beast.