Hi Arup,
Yes, absoutely - you can use different RD for the same VRF on different PEs. In fact, if you have chosen to use the PE_IP_Address:Customer format of the RD then logically, the same VRF on different PEs will have different RDs because the PE addresses themselves are different.
There is no obvious advantage or disadvantage to having the same or a different RD per the same VRF on different PEs. The RD is a tool that allows BGP to differentiate between identical prefixes from different VRFs on a single router. However, the value of RD has no influence on how the prefix will be assigned to a particular VRF on the destination PE. For this, route targets are always used.
There is one specific use of different RDs: Advertising multiple paths to a single multihomed VRF site. Because to BGP, the entire value of <RD><Prefix><Netmask> is used in the best path selection algorithm, if two PEs connected to the same VRF site used the same RD, destination PEs and route reflectors would choose and advertise only one of them (remember: BGP always selects and advertises only a single best path). With different RDs, destination PEs and route reflectors see formally different NLRIs, and they perform the best path selection for each of them individually even though the actual <Prefix><Netmask> is the same.
However, for simple VRF deployments, having a unique or identical RD on two PEs for the same VRF makes no significant difference.
I hope other friends here will add their own thoughts about this.
Best regards,
Peter