Constantine is not modelled on the disappointing 2005 Keanu Reeves movie, also called Constantine. Nor is it an adaptation of DC Comics' current superhero comic book, Constantine, set in the rebooted New 52 DC Universe. The TV show very clearly goes back to the source material, the 1980s DC/later-Vertigo comic series Hellblazer, written initially by Jamie Delano and based on the character John Constantine created by Alan Moore, Steve Bissette, and John Ridgway in the pages of Swamp Thing. The leading man looks just as he does in the comics, with his familiar trenchoat and tie, and he acts broadly the same way too. Just as crucially, his backstory draws heavily from Delano's Hellblazer run. This Constantine is riddled with guilt and fearful for his soul because he failed to save a girl named Astra in Newcastle from the demon Nergal.
This means that the the TV adaptation of the comic is actually more faithful to the source material than the current version of the comic -- but only in broad strokes. In actual execution, this TV show is not the mature affair that the Vertigo comic offered. This is not a cable television supernatural show. This is more like... a Supernatural show.