Alright, sitting at a computer I can give a fuller response.
Basically this boils down to a different vocabulary and theological approach to the issue of God’s transcendence. Aquinas recognizes that God is transcendent, but also that we partake of Divinity and will “see God face to face”.
In the Latin theological language Essence has a broader meaning than it does in Palamas’ Byzantine theological language, and so the Divine Essence includes things like Divinity, which Palamas excludes from the Divine Essence. For Aquinas, everything that is a “feature” of God is the Divine Essence, and God’s transcendence is preserved because humans can only partake in a “limited” way in Divinity through Grace. Thus we share in Divinity, but we don’t “comprehend” Divinity and we don’t “become” Divinity; in Aquinas’ terms we participate in Divinity.
Palamas gets around the same problem of God’s transcendence by making a distinction between God’s Divine Essence, and Divinity, which is the Divine Energy of that Essence. For Palamas, the uncomprehended, infinite aspect of God is the Essence, and that which is participated is the Divine Energy; the Divine Essence can’t be known or seen, according to Palamas’ use of the terms, because in his definitions to know and see include comprehension. It’s important to understand, however, that this distinction is not any kind of separation for Palamas, any more than the distinction between heat and fire means that fire is separate from heat. Heat is still an integral aspect of fire, and follows on the very essence of fire, but the two can be conceptually distinguished. To experience the fire, we experience the heat; the “essence” of fire touches us by heat.
So when Aquinas says that we experience the Divine Essence, he is basically including the Divine Energy (as Palamas defines it) in the very definition of the Divine Essence, and he is not saying that we
comprehend the Divine Essence, merely that we participate in it and experience it, just as we experience fire by heat, and participate in fire by growing warm by the fire. Whereas Palamas would say that we know the heat, but we don’t know the fire, because he makes the distinction between the essential attribute and the fire, Aquinas says we know the fire by sharing in the heat, because he includes heat in the essential definition of fire, but we don’t comprehend the fire because we know it in a limited way.
So they are both getting to the same problem from different approaches: Aquinas makes the distinction in the creature’s experience, and Palamas makes the distinction in God, but the two are not contradictory because they are using terms in different ways and expressing the same mystery, namely that God transcends all creation and is uncomprehended, yet creatures share in Divinity through Grace (and in our very being, according to both Palamas and Aquinas).
Does that help at all?
Peace and God bless!