The DHCP server on the opposite subnet is unlikely to be able to serve
an IP address at all without the router configuration being set up
with an "ip helper-address" (Cisco talk) or if the opposite network
has a DHCP relay set up. DHCP broadcasts are not normally sent over
routed networks. If DHCP A has scopes for both networks, and DHCP B
has scopes for both networks too, obviously the first to respond with
an address would be the local DHCP server. It would normally give an
address from the range that is in the same subnet as its IP. However
if the request came via a router configured with an "ip
helper-address" or from a DHCP relay, then a field in the DHCP
"broadcast" indicates that the request is for the other network, and
the server offers an address from the appropriate range.
Hence, even if the local DHCP server is down, then the remote server,
if accessed by a router with "ip helper-address" or via a DHCP relay
should give an address in the correct range (from the correct scope).
So whatever happens, the sites should be served with the correct IP
addresses and other info.
Cheers,
Cliff