I think, ECGI comes within the "Initial UE message" plays major role while selecting SGW for an UE. MME objective is to minimize the chance of SGW relocation based on current location of UE within E-UTRAN. While TAI receives in "Initial UE Mesage" help MME while assigning TAI list to UE and helps to MME while paging procedure when UE is in idle mode.
Looking for others to respond.