Welcome to the first in what we hope will be a long-running series where you get to choose the innovator of the week. This week we pit marketing and search giant Google against the now-disbanded hacker group LulzSec.

Here is some background on the two organizations and how they made waves.

Google: The Internet search giant launched its new social network Google+ this week, offering a limited number of invitations to prospective users. This is not Google’s first foray into social media, and the field is relatively crowded. So it may be worth asking just how innovative this new product is.

While Google+, or G+, was the big headline for Google this week, the company also hosted the Summit against Violent Extremism, a conference in Dublin that was headlined by ex-Neo-Nazis and former Islamic extremists. The goal of the conference was to introduce new ways to combat radicalism globally. The Washington Post’s Allen McDuffee reported from the conference, which featured graffiti artists, video productions and more than a dozen panels.

And then there was “Swiffy,” the Google application that turns flash files into HTML5, allowing them to be used on devices like iPods and iPads, neither of which supports flash. The development may deal a significant blow to BlackBerry tablet maker Research in Motion, which has heavily marketed its PlayBook on the fact that it supports flash while Apple’s more popular iPad does not.

LulzSec: Last Saturday (yes, we’re reaching back a bit), LulzSec ended 50 days of online mayhem, after having hacked into PBS’s Web site, Sony’s PlayStation Network and even the CIA. They released thousands of usernames, passwords and other personal information to the public. The Post’s Elizabeth Flock has a timeline of the group’s numerous hacks.

By the time LulzSec disbanded, three days after an alleged member of the group was arrested, it had left a sea of digital destruction in its wake. LulzSec is not the first hacking group to go on a spree (and won’t be the last). But they uniquely and effectively leveraged Twitter to inform the media and general public of their work — to say nothing of the breadth and scope of their attacks.

While there’s no question the group crossed the legal line, they changed the game of black-hat hacking.

But whether they were more or less innovative than Google is something we leave to you.