Soundwise, no comparison. The Klipsch ProMedia Ultra 5.1s are not only superior, but arguably the finest computer speakers you can buy.
What separates Klipsches from most other computer speakers on the market is their unmatched frequency response. FR is the single most determinative factor in how a speaker sounds, as it tells you what frequencies of the audio spectrum will actually be reproduced --
at a sound level you can actually hear -- by the speakers.
Klipsch is one of the few mfgrs that actually tells you --
accurately -- what their speakers' frequency responses are. If you look on their
site, you will see the ProMedia Ultra 5.1s reproduce frequencies between 25Hz and 20KHz,
plus or minus 5 dB. That "plus or minus" spec is
crucial -- what most other computer speakers do is quote a frequency response, but they intentionally leave out the plus/minus qualifier. They do this on purpose because although their speakers may reproduce, say, frequencies down to 25Hz or 30Hz or whatever, the decibel level rolls off dramatically at a much higher frequency (say, 50 or 60Hz, typically). So what happens is that yeah, a measurement can be taken showing that the speaker reproduces frequencies down to 25Hz or whatever, but the frequencies below a certain point (50 or 60Hz or whatever) are so weak that no person can hear them. Thus, it's useless to have a speaker system that on paper can reproduce frequencies down to 25Hz if everything below, say, 50Hz or whatever is inaudible. And the same rationale applies to the high frequencies.
Klipsch publishes their FR specs
with the plus/minus qualifiers. On the ProMedia Ultra 5.1s, it's plus/minus 5 dB. Thus, a worst case scenario is that these speakers will reproduce all frequencies from 25Hz to 20KHz and the most the sound level will drop off at those extremes is 5dB. I'll bet you any amount of money that if you could even
get Logitech to tell you how much thier sound levels drop off at the ends of the audio spectrum, they'll be down far more than 5dB. If they weren't, Logitech would eagerly publish those specs.

They get away with not doing it because the masses (particularly gamers) don't know much about audio or how to read a frequency response spec.
Here, incidentally, is a link to Logitech's page showing the Z-5500s. Scroll down to the specs section and look at the frequency response spec. As I explained, there is no plus/minus qualifier with the FR spec. As such, the numbers are utterly meaningless.
BTW, there is very little -- and I mean VERY little -- musical content below 30 or 40Hz. Only very low-octave bass notes go that low, and those are typically found only in orchestral music or the like. If a speaker system will reproduce frequencies down to 40 or 30Hz, accurately, that's good enough for all but the most golden-eared listener listening to the most demanding music there is. And with high frequencies, typically only small children (and dogs) can hear frequencies out to 20KHz. Most adults can only hear frequencies out to 15 KHz or so, max, so anything beyond that is moot.
Having said all this, there are other factors in how speakers sound. Second to FR in importance is THD, or total harmonic distortion. Klipsch speakers are renowned for having extremely low THD ratings on their high-end speakers. The same can't be said for Logitech.
Those Logitech Z-5500s also use only one driver in their satellites, which means one driver to handle the midrange and high frequencies. This is nearly always inferior to a 2-driver set-up (like the Klipsch ProMedias use), as an audio compromise must be made when one driver has to handle both mid- and high-frequency signals. Klipsch's Micro-Tractix horn used for the high frequencies (similar in function to a traditional "tweeter") is renowned for its clarity and accuracy (although it does suffer a bit in terms of off-axis performance, like if you're far off to one side of the speakers rather than in front of them). And their midrange drivers are known for their smooth crossover from the subwoofer.
Also, I don't have time link to them right now, but Klipsch subwoofers are pretty much unmatched as well. Tight, clean, non-muddy, powerful bass is what you will get with a Klipsch ProMedia system. Boomy, muddy bass is what you usually get from other computer speaker subwoofers (although I won't say that about the Z-5500s since I haven't listened to them myself or seen any specific,
credible reviews on them).
Gotta get back to work here, but there's a primer on some things to consider. I doubt if the Logitechs would sound terribly bad or anything, but from strictly an audio-reproduction quality standpoint, the Klipsch ProMedia 5.1s should outperform the Logitechs by quite a bit IMHO. For "computer speakers," my opinion is that they are about as good as it gets, although some Gigaworks [made by Cambridge Sound Works] could arguably give them a run for their money. But that'd be best left to another thread :laugh:.
Hope you find this helpful.
Ken
Edited to fix a typo.