I find it interesting that 1980's UK had a more capable army than Argentina, the UK being a peacetime European country (albeit with considerable offshore possessions...) compared to Argentina with a ruling military Junta and various ongoing local conflicts with neighboring countries.
The UK traditionally is among the top 5 countries with their commitment to defense as measured by military budgets. This is both due to their historic defense culture and the threats that culture is safeguarding the country from. In 1982 the Cold War was still in effect and the UK was and remains an important NATO ally, then against the Soviet Union.
More importantly though is the UK's ability to project power removed from their borders as demonstrated by the Falklands campaign; a capability which the UK still maintains. The UK remains one of the top 3 countries in the world with this capability behind only the US and France.
To project power 1000's of miles removed from your borders is really a capably not many countries possess. China for most of their post WWII history while having one of the largest army's on earth at times, has never possessed the military capacity to project force just 100 miles off their coast and successfully engage Taiwan.
Argentina traditionally is not among the top 20 countries in defense spending. Still in 1982 Argentina had about 220 first and second line combat aircraft to call on and a primary concern of the UK was they only had 40 navy harrier aircraft in their fleet sent to the Falklands. Worse because the fleet operations went 24 hours only 20 Harriers were available for operations during the peak of the conflict in April and May of 1982 at any given time.
The Harriers were new, untested in military action and subsonic. That was a major concern in that conflict for the UK. Turned out unfounded though with the UK knocking out about half the Arginine air capabilities within days of the UK landing May 21. Their Harriers performed very impressively.
I remember the Falkland's war. The Argentine military used French Exocet missiles to great effect. The British to their credit proved the effectiveness of their subsonic Harrier jump fighters even against Argentina's faster Mirage fighters.
Britain's primary difficulty was they had no fleet carriers only smaller jump carriers. This meant the UK could not use their AWAC's (Airborne Warning and Control System) planes, which can view hundreds of miles of airspace surrounding their fleet, to safeguard their ships from Argintina's Air Force. The AWAC's unable to launch from the smaller carriers. The UK had to rely on less capable radar which left their ships vulnerable to Argintina's fighters pop'ing up on the horizon and shooting off anti ship Exocet's at them. This proved to be a costly compromise, as the UK lost 8 ships sunk, another 7 severely damaged and had to be retired. Once the UK took the Falkland's back however they brought in their more sophisticated AWAC planes and based them on the Falklands airbases and Argentina never again successfully threatened.
One other interesting bit about that war was that the United States declared themselves neutral and sent the American Secretary of State, Alexander Haig off to conduct shuttle diplomacy to avoid a conflict. In the background though the US told Thatcher she had a blank check for any aid she needed. The US refuelled the British fleet on the way to the Falklands, provided satellite information on the Arginine military. The provided then sophisticated stinger missiles which allowed individuals to shoot down Argentina combat aircraft, and finally they provided the munitions which the Harriers would use to engage in the coming air war. Advanced sidewinder missiles, all delivered to the UK's fleet while in route to the conflict.
CIA files reveal how US helped Britain retake the Falklands
President Reagan at first said the US would be impartial in the conflict between two of its allies. But on April 2, 1982, the day of the Argentinian invasion, he sent Mrs Thatcher a note: “I want you to know that we have valued your cooperation on the challenge we both face in many different parts of the world. We will do what we can to assist you. Sincerely, Ron.”