Is it an Obligation to attend both the Easter Vigil Mass and the Easter Sunday Mass

The faithfuls are highly encouraged to attend the two. Because, during the vigil Mass, it is life affirming to see the Church perpetuated in Catecumens, and also to hear the entire history of salvation through the scripture.
The Easter Saturday vigil, is just like any other anticipatory vigil for a Sunday, thereby, it is not an obligation.
Easter Sunday however, is a joyous celebration of the resurrection, and under canon law and according to the Catechism, going for Easter Mass fulfils one’s obligations for the Sunday.
Moreover, it is not an obligation to attend the Easter Vigil as long as you will attend mass on Easter Day, but it is a very beautiful way to celebrate the Resurrection.
Because, according to the Code of Canon Law (1248) a person who assists at a Mass or participate in a Mass which is celebrated anywhere in a Catholic rite either on the feast day itself or in the evening of the preceding day satisfies the obligation of participating in the Mass.