Obama beats Romney on the social media site, a new study shows.

Tweets and Facebook FB, +0.78% posts about President Obama and Mitt Romney tend toward criticism more than praise. But when a candidate is getting cheered on social media, chances are, it’s Obama, according to a new study.

Twitter users don’t pull their 140-charcter punches. Of all the tweets about Romney posted in the eight weeks ended Oct. 21, 58% were negative, according to an analysis of nearly 2,500 online conversations by the Pew Research Center. That’s compared with 45% of Obama-related tweets. “On Twitter, the conversation about the campaign has consistently been harsher for Romney than for Obama,” the study says.

Obama’s Twitter traffic suggests he’s holding the support of female voters, experts say. Female Twitter users outnumber males by 53% to 47%, according to one recent analysis by a social media firm, and the average user is a 28-year-old female. “Given Romney’s pro-life stance, I can’t imagine he’d fair very well among women in their 20s,” says John Bonini, content marketing manager of Impact Branding & Design.

Election 2012: Who wins the social media race?

Trends are similar on Facebook. Roughly 62% of Romney posts and 53% of Obama ones were negative, Pew says. Many Facebookers cut Obama some slack after the first debate, the Pew study says, even though the mainstream media was highly critical of the president’s performance. On Facebook, Pew says, the tone actually improved for Obama throughout October.

Of course, Obama and Romney remain neck-in-neck in official polls. Obama leads Romney 48% to 47% — a difference of just seven voters among a pool of 1,475 surveyed, according to the latest Wall Street Journal/NBC poll. But Twitter and Facebook cannot be dismissed entirely, says Michael Cornfield, acting director of the Political Management Program at George Washington University in Washington, D.C. “You can be sure both campaigns examine social media metrics to see how well their messages are circulated,” he says.