Nirvana take this hands down. They took the grunge scene and made it mainstream, at a great personal cost to Cobain.
They wrote songs that people could relate to and even now, Nevermind still sounds fresh and new 15 years on. Plus, nearly every band out there now cite Nirvana as a great influence on thier music(with bands like Red Hot Chilli Peppers and Queen)
On top of that, it helped the career of one Dave Grohl, whoo seemingly cannot do a thing wrong when it comes to making music, that guy has been involved with so many bands in the past 10 years, like QOTSA, Tenascious D and of course, Foo Fighters.
Jimmy Eat World I have never rated, when they had a few songs, I thought, meh, they sound different but nothing special. But saying they influenced the new pop/rock trend is laughable. Bands like Oasis and Greenday took rock music (rock in its many forms, granted) and made it popular again with songs about excess and summertime.