Andrew, welcome to the forum!
The Logitech unit is listed on their website as being able to supply 62W RMS into 8 ohms to the front speakers, but that's with 10% total harmonic distortion (that's a high enough percentage that you would notice it). I might have missed it, but I don't see the power output for something in the range of 1% THD. However, the unit is rated at 8 ohms, and the Cambridge speakers run nominally between 4 and 8 ohms, so it could probably power them. How well it would sound is hard for me to speculate about given the specs.
IMO, if you can't tell really really good music from just good music (which, I honestly think that you could), then stick with the Logitech set-up. Regardless of that, if you're using it just for your computer, then the Logitechs are probably just fine...if not great. That's a nice system, especially when you're sitting close to the speakers like you do at a computer. I have some Creative speakers that cost about $100 that do the trick for me.
Adam