Tool would be an awesome band if it weren't for that weird-azed music they play. Gunny: "Sober" would be the only one most people could name, if any.
Forty six & 2, Eulogy, Schism are my favorite Tool songs, but honestly I still prefer the Foo Fighters... I've known about them longer. Grew up listening to their songs... I know more about the band, and I know more of their songs. Best of You, Learn to Fly, Everlong, Monkey Wrench, All My Life... probable some of their better songs.
Hmmm another tough one. Tool is by far the better band, technically- but foo fighters does have the catchy songs that are much easier to listen to. FF would get the vote.
I'd go with FF as the better band technically. They have two of Rock's greatest drummers. Tool's bass player may be better but the rest is pretty subjective..