It's foolish to compare the Falklands with Diaoyu Islands. The Falklands are inhabited. You can station a garrison there to ensure territorial control. The reason the Falklands War started was because Argentine started a shooting war with the British garrison on Falklands.
In the Diaoyu conflict, who is going to fire the first shot? And more importantly, for what reason?
Here are my reasons for the comparison. Feel free to rebut or comment as necessary:
1- The remoteness of the potential battlefield in a Japan - China clash in many ways resembles the remoteness of the South Atlantic and the situation both Britain and Argentina faced in applying forces to the Falklands
2-A clash in the air between the JSDF and the PLAN would be between beyond visual range aircraft and might not involve much close in dog fighting
3-The Japanese might establish an exclusion zone around the islands warning the Chinese not to violate Japanese waters and airspace You will recall the British did the same thing around the Falklands and used the HMS Conqueror to sink the light cruiser Belgrano as it attempted to violate the EZ.
4-The JMSDF is a professional organization and their submarine forces are considered one of the best in the world. Sinking a PLAN ship would be a very provocative act but would not be outside of the ideas of war at sea in the event of a crisis
5-It is unlikely that the crisis would escalate into a nuclear confrontation because the PLAN would be seen as weak if they had to go nuclear in response to an attack on one of their ships. Remember the British lost many ships and still kept the Falkland war contained as a conventional war. The Chinese would be under pressure to do the same
6-Like the Falklands you have one side with nuclear weapons and one without. That would be a nuclear armed Britain and a non-nuclear Argentina
7-Like the Falklands the United States would be supplying one side, Japan. In the Falklands war the U.S. provided the British with military equipment ranging from submarine detectors to the latest missiles. You could expect the same behind the scenes help for Japan.
8-Like Argentina the Chinese have a nascent maritime ocean surveillance system and and would be hard pressed to locate and hold track on the JMSDF
9-Like Argentina the PLAN has a poorly developed ASW force and would be at a disadvantage combating Japanese submarines
10-Japanese E-767 AWACS and KC-767 tanker aircraft would put the PLAN forces at a disadvantage.