Just based on an IP address it is not possible to check if they belong to the same device. If you were to be in the same network(subnet), you could compare the MAC addresses and see if they are consecutive, which would give you some guarantee.
If the remote router has some sort of service running which allows it to be identified (SNMP/Webservice with unique hostname/Telnet banner etc.) you could use that of course.
You could try running
nmap against both routers and see if the results are the same, which could mean it's the same device, or that the remote party has configured 2 routers with exactly the same settings.