Ministry is another band I'm not very big on, but one that I can respect. I can respect their following and what it's dedicated to. Just not a very big fan myself, though alot of people assume I am when I tell them some of my favorite artists.
That being said, Blur is clearly superior in my book. Along with Oasis & Pavement, these guys all but re-invented British rock, and created the genre of Britpop. They were nearly as popular as Oasis for awhile, but when Oasis became the #1 Most Popular Band on Earth, they were ignored. Until "Song 2" came out, which most people remember as the sports anthem with the chorus of "Woo-hoo!". That wasn't even their best work.
Parklife and Modern Life is Rubbish are two of my favorite albums, and almost never leave my stereo's side. What's even better is how consistent of a band they are, one that has yet to release a bad album. The modern ones have been declining in quality, but they'd still be masterpieces in most other modern rock band's catalogue (I'm looking at you Nickelback).
Blur gets the vote here from me. Truly great band.