vCenter 5.1.0.b was released on 20.12.2012 and we are using vCenter Server 5.1 Update 1a (released on 22.05.2013.)
The issue was resolved by modifying Base DN Group in identity source of for the AD. So I changed the source from DN=DOMAIN,DN=LOCAL to CN=BULITIN,DN=DOMAIN,DN=LOCAL and this worked fine.
Note to VMware: This clearly a bug as I was able to log in using vSphere Web Client but was not able with vSphere Client.
