If both IPs are answering to the same name, then go ahead and use the same certificate on both. It doesn't gain you anything to get a second certificate with the same name on it. There are no security weaknesses introduced by using the same certificate on two IPs on the same server.
The only possible difference is if you ended up needing to revoke and replace one certificate you'll end up revoking/replacing both, but if one cert on your server got compromised, any other certs on that same server are probably suspect too.
Upon re-read, it looks like you're talking about the cert on two separate systems - the load balancer will terminate SSL and pass HTTP back to the actual server? And the server will have the cert itself to terminate internal connections?
My answer doesn't really change. The threat environment isn't worsened all that much by you pasting the key into the load balancer over (usually) secure HTTPS, and if the effluent hits the aerator on either system, you don't gain much security or convenience by using different certs.