I have not heard the HD555, but I can give you my impressions of the K240 Studio.
The K240S is a very warm, bassy can. It has a laid-back presentation, but manages to sound excellent for rock/metal. The midrange is this headphone's strength. It's sweet, rich, and agressive when it needs to be. Trebles on this headphone are slightly recessed and lack finer detail. They are also never fatiguing. Bass is what most would consider the worst aspect of this headphone. In comparison to other headphones it's loose and doesn't have the impact of other cans. Properly amped, however, I think it is very natural-sounding. Soundstage on the K240S is fairly limited, so while this is fine for rock/jazz/rap/pop it doesn't do particularly well with most electronic music (trip-hop aside) and classical music.
I would highly recommend these headphones if you're looking for a headphone that will give you the most fun-factor for the buck, and if you listen to either some form of rock (classic rock especially!) or jazz. I don't listen to much rap/pop, so I can't comment.