Personally, I would say that the Front Line tie-in stands out the most and as the most original. Although some readers might prefer the superhero perspective, what Front Line does is it removes itself from the physical 'front line' of war and places it within the media's 'front line' of newspaper representation of the events, as conducted through the Daily Mail and our (vastly underated) protagonist of Phil Urich - which is an especially crucial element within modern society. I definitely understand why some might prefer not to read the more political perspective, but especially with the outstanding writing by Paul Jenkins, it's worth checking out. There's back-up stories, including a five-page one in each issue which juxtaposes the superhero Civil War against a real-world conflict. In this case, it's the American internment camps during the 1940s which held prisoner to Japanese American citizens. It's grouped together with an anonymous poem written in 1943. It's not very relevant to the Civil War storyline at all, but if one ignores Spider-Man's presence to the right of each panel, it's a moving piece of American history drawn by Kei Kobayashi which really receives no attention.
Fantastic Four is probably the least-useful of the tie-ins, as ASM spotlights Peter and Tony's partnership, whilst New Avengers shifts its focus to Captain America (the cover star), a perspective not really covered within the tie-ins in the Captain America, which looked more at the wider cast of Sharon Carter and Bucky.