All three have a criminal background, as Cole was arrested on unknown charges, although it's possible from resisting arrest as explained he and Zeke ran from police, Abigail was a long-time drug user, and Delsin frequently vandalized walls and billboards.
All three had siblings, Cole, with a yet-to-be-named younger brother, Abigail had an older brother, Brent, and Delsin had an older brother, Reggie Rowe.
All three are in the same age- range in their respective games, Cole being 27-28 in InFAMOUS, and InFAMOUS 2, Abigail being 21-22 in First Light, and 23 in Second Son, and Delsin being 24 in Second Son.
All three had issues with their parents, Abigail hating hers for turning her into the DUP, Cole claimed he walked out on his father, and got a job as a bike courier solely to anger them, and although it's not specifically stated, it's suggested Delsin had problems with his parents, possibly over their favoring of Reggie.
Both Cole and Delsin have tattoos on their forearms, and feature Sly Cooper on their attire.
Cole - The Demon of Empire City/The Patron Saint of New Marais, references to Cole's actions in the respective cities, since Cole caused the deaths of thousands of citizens in the Empire City Blast, and his role in liberating New Marais from Bertrand and The Militia.
Abigail - The Angel of Death/The Grim Reaper/Laser Girl, references to her high kill count during the events of First Light, and her power over Neon.
Delsin - Banner Man, a reference to his tendency to tag walls and banners with his spray paint.