Logitechs tend to have a single fullrange driver in their satellites (such as a single 2.5 or 3" driver) and they will be a little limited in the midrange (which is predominantly from 5-8KHz). This is a frequency range that 1" tweeters do very well in, and 3" drivers do not. In most speakers, the tweeter starts picking up frequencies at 1.8KHz to 2.2KHz, and goes up to 20KHz, so that gives you an idea of what the tweeter is good at, and what a 2.5-3" driver should just not try so hard at.
I would probably suggest the Altec Lansing MX5021s at this price range, as they have dual 3" drivers (audio theory suggests two drivers of the same size will, all things equal, halve total distortion at a given volume level) as well as 1" tweeters. Though, I haven't checked PC speakers in about a year or two, so I could be behind the times (not likely, considering the PC speaker industry moves like a snail compared to commercial audio...alot of updates in design and looks, not much progress in the form of actual acoustical improvements...)
If you want a longer term investment, the Klipsch iFi might do for you, they are of higher quality drivers and subwoofer than traditional PC speakers, cerametallic as they call it, stiffer and less distortion-prone than the usual paper drivers, though they will probably run you around $180-200.