Social network has superior directing and writing IMO. But they are similar in many respects.
PoSV simply tells the story in a pretty straightforward way, while TSN is structured more as a search for the true story. It's structured as a bunch of flashbacks from the depositions of Mark, Eduardo, and the Winklevoss twins. Each party tells their version of things, and as a character says at one point, 15% of typical testimony is lies, the remaining 85% is exaggerated.
The movie doesn't try to take sides, and leaves it up to the viewer to decide who was right and wrong (if anyone.)
Nearly all of the technical merits (writing, acting, production values) are better with The Social Network, though the leads in Pirates do well. Pirates tells a much broader story, and Steve Jobs and Bill Gates make more interesting characters. (Woz and Paul Allen are played straightforwardly, and Ballmer is recognizably Ballmer.)
It's quite notable that Pirates tells a broader and more interesting story than The Social Network despite The Social Network being far more fictionalized.
If you're looking for parallels to contemporary startups, The Social Network is a bit more on point--Pirates goes farther back into the founders' backgrounds and forward into the lives of Apple and Microsoft as established companies. But both are still great.
