Here is a little more information...

I downloaded another (weaker) offline browser product to 
test.  The job that took 4 minutes took ~30 seconds with 
this product against the new server -- roughly the 
performance improvement I expected.

So, it doesn't seem to be just an Apache issue -- Apache 
runs fine with other products.  It seems to be an issue 
with the combination of WinHTTrack and the Apache 2.0 
running on Linux.

Why would WinHTTrack be so slow against the Apache 2.0 
server on Linux?  Again, the exact same job runs fine 
against the Apache 1.3 server on Windows XP.

I really don't want to change products.  I haven't yet 
found another product that provides the level of control 
and features of WinHTTrack.

Any help would be appreciated.