I got the logitechs after a similar set of questioning. The klipschs do have a tighter bass, and better mids. However, the z-5500 costs quite a bit less depending where you get it (40-120$), has killer connectivity optioins, very crisp sound, and a much better control device (that does look a bit tacky), along with much better sound options and better highs (IMO).
Klipsch connectivity options are terrible. Analog outputs. That's it. Nothing digital. If you use a mac (like I do) no surround sound.
Logitech has a massive set of connectivity options, and the setup is cleaner and more aesthetically pleasing.
The bass and mids sometimes hurt a bit for jazz, (bass gets a bit boomy, and piano especially is an issue to listen to, (for my Oscar Peterson albums I usually end up using equalizers within my computer).
Consider it this way. For music, I'd rate the klipsch at perhaps an 8.4-8.8, and the logitechs around 8-8.4.
The difference is pretty small considering the price diff, and the logitech offering is a great deal more flexible.
Also. consider if you want 2.1 or 5.1 for your computer. For example, Klipsch promedia 2.1 or Harman Kardon soundsticks II sound about as good, but are smaller and cheaper, though they obviously lack the surround capabilities.
Lastly, remember these are computer speakers. I use them for music, but if you are really focused on the musical aspect, towers or bookshelf speakers are infinitely better than 98% of computer speakers.
Hope this helps,
~Molinjir