It depends on the situation.
Froma UE perspective: Are you losing sync ? Are you trying to measure the signal at the UE and trying to do a Handover ? Then keeping track of RSRP and RSRQ is important.
Are you trying to detect interference experience by your UE ? Then you need to check both RSRP and SINR.
RSRP is typically used in Handovers and is communicated between the UE and eNB. SINR maybe internally used either in the enb or ue or both. CQI computation at the UE may use SINR but will definitely use RSRP in one form or another.
While calculating RSRP and SINR, received power is considered.
SINR becomes important when interference comes into the play.