Yeah the reason HK went the way it did was because China could credibly say "Give it to us or we take it". Argentina already tried the take it by force way, when their military was in a much better state than it is now, and there was effectively no military garrison on the islands. Argentina have pretty much zero leverage here.
Hong Kong was a completely different situation as the British signed a specific lease for Hong Kong with a set end date that was known all along. Nothing like that happened with the Falklands.
That's a common misconception, the 99 year lease was on the New Territories, rural areas in the north of HK. Hong Kong Island and Kowloon (the heavily urban bits you think of when you think Hong Kong) were under no such lease, they had been permanently ceded to Britain when it was just a fishing village on the coast.