Hmm... I wrecked Rome and England without problem as Brazil with little army in Prince, and I completely eliminated USA, England, Spain, Sparta, Norway and Rome with Germany on King. Currently destroying China and Kongo, then I'm going to destroy Egypt and Sumeria. I was only defeated by AI twice, once as Spain on King by Sumeria with lots of warcarts as my neighbor, and then by alliance of Sumeria (again with lots of warcarts) and USA as Germany.
In Civ V, England was worthy adversary in my game as Brazil on Prince. And I was totally eliminated as Venice by Russia on King. Oh, and I started to play Civ VI earlier, so I had some skills in wars.
So, I don't think the AI is much better in combat in Civ VI.