Okay, I had something long typed up but I lost it so here is the short of it
Doesn't seem like anyone else here owns the system so I will provide my two cents.
The Logitech Z560 and the BA7800 use different wattage specifications. You cannot compare the 400W straight up with the 98W since they're talking about "Maximum Burst Power" there, and not sustained wattage).
As for the actual speakers themselves. I bought both the Z560 and the BA7800 and I can assure you that the BA7800 competes just fine volume-wise. I did not test them at their maximum volumes as I did not want to kill my ears or annoy my neighbors. Using the BA7800s at volume level of about 10 o'clock on the volume dial is more than enough.
Quality-wise, the BA7800s win hands down. Music sounds a lot better on the BA7800s than on the Z560s. If you want to host a party, well, the Z560s are fine as you won't really care about how the bass from the sub is as long as it is loud and shakes the room. But if you want strong clean and just as powerful bass, I would go with the BA7800s.
From what I have read (I have not owned any other of the more recent systems), the BA7800s are better than the Altec Lansing 641s. In fact, the only systems that are said to be better are the Klipsch 5.1 and the high end Videologic speakers (Sirocco Pro, Crossfire, etc). The Videologic speakers are in a class of their own though, and they should considering their price (Crossfire runs at about $900 I think). These are also rated at 100W but there has never been any dispute as to how much they kick the arses of the competition.
If you want something cheaper, try the older BA speakers. Their 2.1 solutions are pretty good too, better than Logitech's 2.1 speakers for sure. The BA4800 used to be one of the top systems as well, competing with the Klipsch Promedias when they first came out. Do not buy the BA7500 though. I have not tried those but I hear they are crap. All in all, Boston Acoustics has always been up there in the computer speaker market. If any of you remember, they used to be the best, back when Cambridge was top of the line as well. This is my 3rd system from Boston Acoustics and I am completely satisfied.