To my knowledge, we are to do both and more. Sometimes we cross ourselves, sometimes we make a deep bow....and then there are times it is most appropriate to make full prostrations.
The most common place to make deep bows (metanoia) are greeting icons and at Holy God, Holy Mighty, Holy Immortal in the Trisagion prayers.
We prostrate before the Holy and Life Giving Cross on its feast days, before the relics of saints (in many cases), and at the consecration of the Holy Gifts during weekday liturgies, during the prayer of St. Ephraim in Lent and during the Kneeling Prayers at the end of the Pentecost season. As a rule (but with a couple of exceptions) we do not prostrate on Sundays, nor do we kneel or make prostrations as rule between Pascha and Pentecost either at home or in church.
The exactitude of this observance is different from parish to parish...at least in North America.