First of all both the messages have different purpose even both of them are transmitted over common channel (CCCH).
RRC Connection Request message is sent by UE to eNodeB when it was not having connection with the eNodeB for example: UE attaching to the network or for mobile originating and terminating calls.
RRC Connection Request contains the initial UE identity which can be 5 bytes long S-TMSI or random generated number. Along with initial UE identity, UE sends rrc establishment cause to eNodeB to inform the eNodeB that what causing the UE to make RRC connection.
After establishment of RRC connection between UE and eNodeB, if RRC connection brokes (due to radio link failure, rrc reconfiguration failure or handover failure) between UE and eNodeB then UE initiates RRC Connection Re-establishment Request message to eNodeB considering a valid UE context will be at eNodeB. That's why UE send ReestabUE-Identity (C-RNTI, physical cell identity and short MAC-I) along with cause value. By using re-establishUE identity, eNodeB fetch the UE context also check for the authenticity of UE based on the received short-MACI. If eNodeB has context then it will proceed with rest of signalling else it will respond UE with the rrc connection re-establishment reject message.
Now, you can easily make out why both the messages carry different set of information.