Anita
OSPF Priority overrides the router ID so if you set the OSPF priority to above 1 (which is the default OSPF priority) then it doesn't matter what the IP address is. Note also that a public IP is no different than a private IP in this instance ie. OSPF doesn't know which is public and which is private. If the OSPF priorites are equal then it simply picks the highest IP from any loopbacks and if there are no loopbacks from the physical IPs on the router.
As i say OSPF priority default is 1 on Cisco devices at least. Don't know about Juniper.
When you say the 4500/3925/ASA/Juniper are in the same OSPF domain do you mean they all have an interface on a common subnet ? Because a DR/BDR is elected per interface not for the router as a whole.
A further thing to be aware of is if you increase the priority to > 1 on the 4500 and it is not already the DR or BDR then it will not preempt the existing DR/BDR. You need to reset the OSPF processes for this to happen. If you don't want to do this then an easier solution is to set the ospf priority to 0 on the devices you do not want to be DR or BDR. If a device is a DR/BDR and you set the priority to 0 under the relevant interface it will relinquish it's role without you having to reset the OSPF processes on the devices.
If however you want to set the DR/BDR explicitly by using a greater priority than 1 then you may well need to reset the OSPF processes on the devices. I'm not sure what Juniper use as a default but setting the Juniper to OSPF priority 0 will mean it will become neither the DR or BDR.
Jon
