Let’s make some distinctions first: In the East, the liturgy that Roman Catholics call the Mass is called the divine liturgy. Some churches in the East are in union with the Catholic Church and others are not. Those that are in union with the Catholic Church are called Eastern Catholic; those that are not are ordinarily called Eastern Orthodox.
The Consecration of the Eucharist during the divine liturgy of both the Eastern Catholic churches and the Eastern Orthodox churches is valid. A Catholic of the Roman rite of the Church can attend an Eastern Catholic divine liturgy and receive Communion during that liturgy without problem, and the Eastern Catholic divine liturgy would fulfill the Sunday/holy day obligation. Although Catholics can occasionally attend Eastern Orthodox liturgies as a guest, those liturgies do not fulfill the Sunday/holy day obligation to attend Mass. Catholics ordinarily should not receive Communion at an Eastern Orthodox divine liturgy, though there are circumstances in which this is permitted.
If you have trouble discerning whether a particular Eastern church in your community is an Eastern Catholic or an Eastern Orthodox church, call your local diocese and ask.