I don't know of broadcom but here what i can tell about e1000 :
e1000 does not support the mii. Do not expect mii-{tool,diag} to work.
I know for sure that those link are in full duplex Giga mode (switch
configuration and benchmark).
Anybody knows a way to get the real state of these interfaces (other
tool ? /proc/* ? etc...)
ethtool (packaged) is able to view the state of e1000 interfaces.
The driver allows you to change them at load-time.
http://www.intel.com/support/network/adapter/1000/linux/e1000.htm
Furthermore, intel has some tools available that can change negotiation
parameters on the fly (and other things like VLAN or teaming) :
http://www.intel.com/support/network/adapter/1000/linux/procfg.htm
Hope this helps...