LulzSec is certainly a skillful hacking group. It bested big corporations like Sony, government agencies like the CIA, and even a cyber securities firm.
One could make the argument that it's easier to be an anonymous group that attacks a target rather than the target defending against cyber attacks (the old we have to be right every time while they only have to be right once argument).
Still, LulzSec proved that most websites can be DDOSed down at will and websites you'd think are secure really aren't that secure. Perhaps the biggest real world impact of LulzSec is reminding netizens to never recycle passwords and be careful of the personal information they reveal online.
However, what it hasn't done (yet) is reveal classified government information, which it vowed to do in its Operation Anti-Security manifesto.
Wikileaks was an organization that did exactly that. It famously leaked US diplomatic cables that contained classified, shocking, and previously unseen information.
The world learned that the US ordered its diplomats to spy on UN Secretary-General Ban Ki-moon (and others) and the King of Saudi Arabia urged the US (numerous times) to attack Iran to destroy its nuclear weapons program.
More importantly, the cables have been credited with providing some of the sparks that started the 2011 Middle East uprisings.
Foreign Policy said the following about Wikileaks and the Tunisian revolution:
The candid appraisal of Ben Ali by U.S. diplomats showed Tunisians that the rottenness of the regime was obvious not just to them but to the whole world -- and that it was a source of shame for Tunisia on an international stage. The cables also contradicted the prevailing view among Tunisians that Washington would back Ben Ali to the bloody end, giving them added impetus to take to the streets.
So big was the impact of Wikileaks on the world that many thought Wikileaks founder Julian Assange should have been the Time 'Person of the Year 2010,' not Mark Zuckerberg.
Contrastingly, LulzSec's activities so far have just embarrassed/annoyed government officials and corporations and put thousands of netizens in danger of spam and identity theft.
However, if it actually delivers on its threat of exposing government secrets, get ready for another wave of international uproar.