I found the problem!
Printing to the network printer was also very slow. So reads (receiving) through the NIC were fine in all cases, but writes (sending) to the other Win7 system and the printer were painfully slow. I started searching with that in mind and found the answer at answers.microsoft. I disabled "Large Send Offloads (IPv4)" in the NIC and now everything is working as it should.
A little more checking and apparently the Realtek NIC drivers turn this feature on, whereas the Broadcom NIC drivers on the other Win7 system do not, and it was disabled there. Enabling LSO on that system caused it to start acting the same with slow writes to the other Win7 system and printer, but normal read speeds.
So both are disabled now and life is good.... time for a beer.
** Sent from my rotary dial phone using TwirlaWord **