See Badger, I'd say Fugazi were more like Hardcore, or certainly straight edge, rather than emo. I know that the term 'emo' is not today what it was some time ago, same thing happens with every kind of music - Velvet Revolver for instance don't sound much like Led Zeppelin but they share enough in common with each other to be classed under the broad genre umbrella of 'hard rock'.
I don't think emo is a bad thing at all. I would say that I don't like a lot of what is currently coming out as 'emo', but I would still stand by my opinion that Saves The Day, in my experience at least, are closer to the modern term of what 'emo' means than they are to say, Fugazi. I can't imagine StD busting out 'Margin Walker' or something.
But at the end of the day, it's all opinions, it doesn't really matter how you label music, music is still music! Fugazi are $%ing awesome, though. Incidentally, I'm just checking out that Sucioperro's myspace thing, giving it a listen.